Black Holes in General Relativity

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PoS(BHs, GR and Strings)001 http://pos.sissa.it/ † ∗ [email protected] Speaker. This research was supported by the Marsden Fund administered by the Royal Society of New Zealand. What is going on (as of Augustinspired 2008) models, at the and interface between observational theoretical astrophysics?personal general relativity, choice string- Quite and focus a on lot. four speciﬁcof In questions: the this Do word black mini-survey holes “exist”.) I “exist”? willhole (For Is to selected make black arbitrary values a hole accuracy? Can formation one and detect evaporation the unitary? presence of Can a one horizon using mimic local a physics? black ∗ † Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

Black Holes in General Relativity and24–30 String August, Theory 2008 Veli Losinj, Croatia Matt Visser Black holes in general relativity School of Mathematics, Statistics, and OperationsE-mail: Research, Victoria University of Wellington PoS(BHs, GR and Strings)001 ≈ ].) 7 r , / 6 m , 5 , Matt Visser 4 , 3 1, though there are . r / m 2 ].) 9 , 8 , 2 Astronomers have certainly seen things that are small, dark, and ].) Furthermore, advection dominated accretion flows [ADAFs] are 2 , 1 Astrophysical Black Holes (from super-massive to stellar); Primordial and Mini Black Holes; Black Hole Entropy; Information Paradox; Asymptotic Symmetries; Anomalies; Attractor Mechanism; Holography; ADS/CFT correspondence. Do black holes “exist”? Is black hole formation and evaporation unitary? Can one mimic a black hole to arbitrary accuracy? Can one detect the presence of a horizon using local physics? • • • • • • • • • • • • • 3. (See, for example, [ / commonly interpreted as probingstill the some spacetime disagreements geometry on down thisCertainly, to point everything observed within 2 so the far community.spacetimes. is (See, (See, compatible for for with example, example, [ the [ standard Schwarzschild and/or Kerr heavy. But are these small,relativity? dark, Accretion heavy disks, objects and really in particular black theirsurrounding holes inner in cutoff black radius, the probe hole sense the of spacetime candidates geometry classical down general to the innermost stable circular orbit [ISCO] 2 Instead of trying (uselessly)to to address address four each specific of questions,currently these these important questions questions topics of representing in black my hole turn, personal physics: choice I regarding will the use this mini-survey 2. Do black holes “exist” ? This innocent question is more subtle thanwhether one one might is expect, thinking and as an the observational answer astronomer,physicist. depends a very classical much general on relativist, or a theoretical Observational astronomer: Black holes in general relativity 1. Introduction This workshop deals with a large number of topics: 1 PoS(BHs, GR and Strings)001 Matt Visser ], or any of the 13 , 12 , ].) 11 , 15 10 non-unitary evolution in the domain of ⇔ 3 ].) Furthermore classical astrophysical black holes 14 Strict event horizon (absolute horizon). Eternal black holes certainly exist mathematically, as stationary ], and unless and until we do so one retains some freedom to pos- 16 Figure 1: But one can always argue that we have not seen direct observational ev- existence of an event horizon. ⇔ . For all practical purposes: Information loss 1 More radically one could just pick one’s favourite “problem” or “oddity” related to black hole The most important thing to realise is that information “loss” is (in and of itself) not a prob- outer communication physics, and use it asstill an excuse has to a speculate. nugget One ofentropy, of and physics black the hiding hole most at physics. abused its issues core) in is this the regard (which relationship between unitarity, information, 3. Is black hole formation and evaporation unitary? lem, it is merelyif a you “feature”. accept the Information standard lossfigure Carter–Penrose is diagram for just the one causal of structure those of things stellar you collapse, see have to live with many standard textbooks in general relativity [ Theoretical physicist: idence of the event horizontulate [ new and different near-horizonwell-thought-out physics. alternative to In standard fact near-horizon doingspecific physics ideas so can of is what give not to observational look entirely astronomers for. perverse, in that a Black holes in general relativity Classical general relativist: vacuum solutions to the Einstein equations. (See,(future for event horizons) example, certainly [ exist mathematicallyon certain as physically the plausible end equations result of of state. classical (See, collapse for based example, [ PoS(BHs, GR and Strings)001l , , l - t r e e e e e n d n n d d y a e a m r n e l e u h h h e o o o n c c n s i o n v i o i t u t t t u p i e i ( . t r t a t a o ‘ c g fi o s t f n i t c o a n a t c p i f y fi i a w t e g r a p s i o e a u a i h s p d r e o n t h . e t , m d w e i e i e n , e p t i t e d p s l a e . n s e o l h v d s i r x w w a e e i t o d t e n o o m l n . h o o i o r o v r l h , i l d l e h r a o r e e v p l t l e d l t d w i o c s e p , a o s d o a t i h i f b d o k f r v t r v e y p d ]. s a o o i Matt Visser a c t e e g m a e p a h ].) Largely r y n n y r i e t a s t l F 22 t t h r o n l o o , h p d s a a , h a i i 23 t n i s o a o . p b p o t f n r t t , l h i o s i h u e n 21 a r a o o e o t a l u t n h u e t o v r b s n a s g p a W i t n e o m v t e o t n e n T i a n e t u f r o n e i e . n n i t t i o i t v e e o i b o s . y I s t e , l b w a c e r i ] f d t o n s t a r o i o e l a 0 d n d . e s p e a e e i l v h e a h h s 1 l a r m n a [ ] horizons, that may make h e r d s a n u r e o n a p i t T h d e e r d k e t h o o o s c e h fi 20 t y f c s t c g n h n r . g t n w o t y a e o a n i d e 1 e k f l a o t n i l l r r d i i c n N m o c d s b o l a e a h e s p o a a n s l l e u i . n r c l t h . g i h o t e t r s o n u s u a t e u n n t b n u s t g e a n o p k t s g g a o i t o m t o s u r c k a e i a i t s r n t a s t fi a c s h a t i t u t g r u a l m a d i c t t t s s s r a s n a o l q t e e s d e o b a i r u r a a l l j c e a e n c p e n l l l l d o b o l r l a g d e b n x a e + m i e P p t s m e e p n u n t e y o i i x J f n a y e t a h s t a x a h i fi h t ], and/or trapping [ e i m r t ! r i r e e v a t v o u h c s 4 t l J h v g i j w e p h e m t e , 19 i o e d t m s t a w t a e p e t h t i t e s c o a e r t e e a s t a m d 3 o e l s s n e d n s o l h d e i i p t t e o t o a n o t e y t k v n s s s a h s k e i t n l r i h i h l i b o n f o c e m l g r e t i o l n T h l o o — a t n n o n e k p t l v l i fi d i r r e e c a c o . r y r h e e t e l g n e l , t e v y t a e c i u i n l d a e m l e t g s t n d w P i s v i i x i d r e r o f s e b h a o ], dynamical [ n t n o o e r d l a o v a t t e v i o - e u e l a l f f l a p e t e r e x 18 e h l i e a o n b o t r e t m c s c e t , r u s h t l e v , a d e m e n w a i e s g c i t s s t r n e y s e n 17 h d f t f a p n e h e u u n a o a t - e , f s l a Standard Carter–Penrose diagram for an evaporating black hole. s t i i m e i m e l b h s y T t s e a m e m a i i m e l c 14 n u w e t a e i t n w h . b a h d s s o g s s s e e n y d l i i e t p r y e + i m r o e e r v t t l a s i s u t n e i I a t t e e i v o e a t n r n h m x o a o l a e t a d l s t e t l n o o o u t a o h t i i Figure 2: s r m i t s h a , h r e a s s i x p l h a m t r s w c p e n x t d e a e i d n c u e — e e 1 l e i p k r o e a r o n n g c y t “The way the information gets out seems to be that a true event horizon never s r c h m u h i a m t u l d h a e r e u t t o n y t s a o p u a t t r p n i g a l p e e t s n h o y h p n l forms, just an apparent horizon.” o d u l r s b n . s s n e l p n a e H ] y i Furthermore, once you add semiclassical quantum physics, specifically Hawking evaporation, As soon as one has an event horizon, one has an inaccessible region, and an external observer But is “event horizon” the right concept to be using? There are many other possible definitions e b d g a s o n a s a i e h i e 1 d h l a h d e h a e i i . n o t t u e h n t 1 i h t F a n n e o o T T s [ i t t t , t q l a n c n (The actual talk given atbe GR17 has found never on been the published, web. even informally, The though transcripts scientific can publication closest in content to that talk is [ the issues again become more complicated,(quantitatively) leading happens to the to so the called information “information youreaches paradox” thought — its you what had final lost state? onceevaporation the is (Whatever evolving unitary black (as that hole seen final fromthen our state there own had happens asymptotically better flat to not domain be be.)the of any abstract outer any to communication), If event his horizon you talk in delivered believe the at spacetime. that GR17: To Hawking quote Stephen Hawking in more physical sense. Even classically,relativity, event simply horizons are because seriously they diseaseddefinitions are in of so numerical horizon general difficult are often to preferable find from a with purely any pragmatic point certainty of — view [ local or quasi-local independent of one’s favouriteloop-based, model string-based, for or the something else, “quantum themany theory last if few that years not would has most seen beevent/ a physicists gravity”, absolute/ consensus now apparent/ whether shift trapping/ seem to dynamical where to horizon think distinction may that be Hawking more evaporation than just is a unitary. matter Thus the must then “trace over”states the become states density hidden matrices. innon-unitary Thus that evolution an — inaccessible at event least horizon region, as (absolute and seen horizon) from for automatically the that outside. leads observer to of pure horizon: apparent [ Black holes in general relativity s o z w e d i i i a e n a : a , i . s o s i 1 a i o s t s l . ’ k u r i r ) c 1 c a c s y e e ] s a a t n a t s i q n d o e e e . r r a o 2 s n a h o r h n l r w ’ h r s s h g e a i t 1 k o y G

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e t P s PoS(BHs, GR and Strings)001 . . - - - r e e e e e a d d h n n l l e e r r i + l u e t v e h o , m i b I a a e r i . t v o n m m s i l e t i e e i ’ w s o fi w . o t r t c s s n p i s n e e s ( o a u m n o e g o a a l e d f s m l c o p - a o r i h i p , ] have e l i e , s e r u . l n h c t k t r r s y s e g w e . In this i e e i g a ].) . I t e a e 25 l s a i i a 2 i l - w u t r i h s a ( f p m y e n Matt Visser s u e o 24 a t d o c u d a w e c i r s s fi p s l i a e i e r k e ’ h m - s n e i x r a k a p h i i h i s e l l c e r c s t - t T u m d o l u e e n i a m l r p t ) o t i r r g e . i d s u c n e g m u i t e m m e n r e i a e e n i s h l o t h i fi r i s t d d c m P t e e e i i x s ‘ a n e l e , s l n r v r k t t e e t i I o a - s a h c t u a i e r u i c e r m e t e n e i g h h ; d n w h c o s a c e v u s h o y t l i m s c a f i t t t n n e e e R a h f i i g P p r r n l t m d t e b s o a e e i c e w a r y e p u g c p l h s s n : e e h m e o a n o e a e n d e t y w h u o I d r r c e y h t t t d e i z l i g r ‘ t u p l i e l s n . r r e t n w e r e 0 i r s a s e n d a a r v a a o e o , it is critically important to realize d i i a c l e o h n o e o l i c h i 3 h o p g h u f t s r a h c c t t g n s e w e g a m r i w o y n r d r n y n h s i n t e t ’ i l h i o n t s o a p n s e t S e i i s t p + s a p m y r o r h t e b x a i l p H a i a o l u a t e l J e e a v n r e l m a n a r p r G w e ! h o g e u r c t a n e u m t i g a C c h o i c a t o g 0 s i J s l p 5 n e i t t i p s o i n 1 a n - d g e l h i f n a h i I s a l c e e t r N l k h t o v o a r n c e i e i t c t e f i s s . w t e a d i p n n w a s d a o e a i e i n p a n s l e l r e s i i a o H f m g p o o d m H n h r l a H o e n n f r t a h e t t r i n s is unavoidable — as is the associated information loss and m o s . o e l t h i e n P l o f s k s f ‘ u n e a a i h 2 o d a e c n t u i t t o e t o s c h i e a t i a a n a a c t l d y u h c a t n l a n u b h a e n s s i y t a t T n n c u c l m i f o a i b o h e l o a i q r e s n o i c . h n t s a r b o o 2 s e , n e f o u e u t w r w s e l o e m h c n g m e e o h p r k t i t o t a e r r n t l v a s r n i r o i g ff e i e u o t e m g e u n ) r . h e r g a n i m a n u w d o y t h i t fi o h a o o w y r n s s d i t t n , t r i e : e a t H H t t o e a s n c d h s e ) e e t p a u t n e o w i n n r e m n i . i h m q c r o o a m r e o i t s h o i t c f S o t e e h t t h z u n ) ffi s y - f e i o s g l t l r . a e e e o e r f Ashtekar–Bojowald version of the Carter–Penrose diagram for an evaporating black hole. . u g e o e i r l g c r n t s o d e o d s t e n v a d a a n s i h u t l c n i e n c r m d e n p i l i n u o n i l e i e a i b u s w S e s n a o s m t ff s s i e o w i m e c m m e e n m n l a i : t i l complete evaporation? a timelike (naked) singularity? a stable remnant? t E s g e n l e l u o s a - 2 c e i r d r b c t As an counterpoint to the standard Carter–Penrose diagram, Ashtekar and Bojowald [ Consider the standard Carter–Penrose diagram for an evaporating black hole, figure o o c m e i u s - a m f • • • . o Figure 3: h i n ) i a p s c r q i W a t r s a b o n e e e G a u m y I o u y u k s y h h p e w r n o s that qualitatively the same sortstring-based of model of causal black diagram hole mightgravity” evaporation. be the Depending shaded compatible on region with of one’s a favourite Planckianinteracting model curvature unitarily string might for muck”, evolving be “quantum or viewed more as prosaically a as “loop a network”, region “strongly of violently fluctuating spacetime. As long as onethen insists the on standard the diagram black of figure hole being defined by an event horizon (absolute horizon), standard picture there is always awith region the of (vertical) “don’t timelike ask line because emerging wesource from certainly of the cannot the endpoint tell” famous of associated tri-chotomy: the Is evaporation process. the endpoint This of is Hawking the evaporation suggested replacing the spacelikean singularity alternative by Carter–Penrose diagram a forAshtekar region the and of causal Bojowald Planckian structure were curvature working ofdrew within — black their the hole leading version framework evaporation. to of of While loop the quantum Carter–Penrose gravity diagram, when they figure non-unitary evolution. Black holes in general relativity of mathematical convenience — ithole may formation be and critically evaporation. important (For to earlier somewhat the related underlying ideas, physics see, of for black instance, [ i I t p a q t f i s s t p l d t F b PoS(BHs, GR and Strings)001 4 ], 20 ]. At a 31 Matt Visser ]. For some older 29 , ]. While the diagram in 28 , . Furthermore, in figure , l : , - 19 - . ) ) s e e a g 3 y n n p l ] n r 3 e y s i o 0 1 n e l h g n o 3 o a d e f i 27 r m g a i i i 2 2 t r e t o w i 1 o r t ( ( p o g [ e e , t k n h y m e f a e e g k l n u=v n e n , s e r n t 0 k k e a d o n k s o d r a e i - 26 c t a flux i u v e e c o a c v t v=v e t t u o o k , a d g a y energy v i l a c r r m 0 T r e n i l i n i b > s static: m=m b - r d i w , remember that all these causal di- t a o o i positive d a i i e t d a o v n p v f 3 s a e t d p H e r v=v radiation: y n a a > r o e m N r a r h e v f a i d 2 f c t a d s p o i r e o g y u=v d s e o a u . a n v F l e g n a r l h d v g v d o i r e V p r t d a e . o v=v c n n i T e k f e ) F h e i d s a g f 0 r y t n = 0 , 5 o d w t y t o o n i e g l . 1 − u a i g n u l m u s r ( h u t m pair creation surface r=r l o t o m o r a e e b t H e i – n e u i g n c d t = v ) n o , a i d d t 0 o i c infinity h h m o a g e t 3 u w 0 e ) o ].) t i l o u t t - future null n 1 r d i i t z g m a m u , p e o , y i s i ( m 2 r ( s l 2 n g y v=v v w w o b d i d 30 o i n < e a o u d n g flat f n g t 6 e n t i , r b − e a r n n v t e > d p ) r o f a d e d e : d o v 2 u r e r surfaces a o i 5 i i z g p a 0 n r untrapped h e c < ( a s g e S r v=v g d r O t e o d t d n e n e i e d n f a i v m e v e e t r a outer s r a a e h 2 s . a w l r r h r ) a ] t r e horizon radiation: positive energy flux u r v r y t n e a o i s i o 7 < f 7 o v h g i f s b o t [ k f c v=v b d t 1 x o o a i n i e e = c i i u i ( l l a s s t b b , y i - 0 s , d e r d c – ∀ F 2 flux inner o l l e o s i a r e a ) energy h l i d s l t negative trapped surfaces s n p m e i n u y 6 n l o radiation: horizon a . d r i s e r T a i s o e t 1 ) d h = a t o e s h d a h i ( l e d r t . t ) u e t t p u a a e k i ) d ( r o n r s r o u infinity o c d past null t e n 5 V e e w n , g e a d i t l m o l c t p r P r . n n g s a ; fi ( b i a o regular centre n o g u o e m e a n : h o i n i o l h o d u i r F t r 5 t i b o m t c g e F a t a flat o T t i l a z p . ( v c n i t i g c h o n i e u e t o d r r t w I t s e G d n l e g i d I l a u o o n f u b a i e h e u a s r fi o p n s w F r h b f u o a t , . ------) ) ) ) ) ) ) ) t t r ) b e e e g g a o a x n d n d s s l s labelled “regular centre” is timelike, and with a suitable choice of coordinates e . s i r s v k t p v 3 4 6 5 9 8 7 2 o v n e i o n n n n m ) r f s n u fi s e a i i i o o , a 1 1 1 1 1 1 1 1 a g i v s d w a 0 a f a 4 t o s e e c o i ( ( ( ( ( ( ( r ( r t i h p l e n d r r a e e t < z ( t r e s a s e a g i i p r l r i c n T a a a r f d e t . s p i y n Hayward version of the Carter–Penrose diagram for an evaporating black hole. H r t t e a F r o l d u y e r v p < , v v a n o o . i h o r a n t r s h l c a a ] d g t n i a c t e s e s t r e h ) c h r c . r = w 7 n n s y o a n o g e c l t [ v i a v < i i 4 o n r a r b e t r n m e g g r a f ( n d t , t i e s o m ! e o c r a ∗ a s e h n m n c s n i . t o d a f n f r l i n n g n i i i t i v g i d n o n . h : u I a o n t e m o n i i t , m g o n a p d t s . t . a d f t o i f t y z a n v o e a 5 d o g r i ∗ p ∗ a i n . a s m i i g n i l o l a , g c z t r d > a r e r v a . i o o g 3 n n a s e c r o n d f n o u m n < m r e e i l d o r i g z h i e o o e 0 p d a n fi . a Figure 4: t i i e r r o at first glance looks rather different from that in figure o r e a t i i o p n i v m h n . r v r s n r v o o 0 0 c t b a p s s g = e d F = r y i a h p a e 0 0 m 2 i T ) u e g o d y v s v 4 ( e t e o i v e ) o e s ) g c a l g m ) 6 ) e l p a i h r a ) > < n c 0 o k r n ( e b g s n n n F l t = = = i n n a h Yet another causal diagram for an evaporating black hole is that due to Hayward [ While there is no event horizon in the Ashtekar–Bojowald diagram, there typically is an appar- m m s i i m y ! i i , e ) ) v v n n e c r a t n e o w < e g t s m e i s ) ) ) 2 e i o i l ( ( n d g , c t v r p = A i v v h l l o v v i e , m n , o v ) v v ( t b g y h o s ( ( p a ) i n n t f p i s l 2 i a l r d n . ( ! ( ( ! a 4 f i t m m v t d p n e v ) h n p o r a e c p t r a n r v i g p e n ( c - ( e ) r c e e r i f c a k l m m m m m c n h o ± + : : p s 2 u a e n while Ashtekar and Bojowald prefer tofigure work with dynamical horizons [ agrams are conformal diagrams — theyadditionally depend are to specified some only extent up on to one’sof a choice the conformal of diagram factor coordinates, that depending and can on be whatpurple used aspect line to of in expand the figure or physics contract one parts iscan most be interested “straightened in. out” In so particular, that the it looks like the vertical line in figure ideas on singularity avoidance, see, for instance [ technical level the main difference is that Hayward prefers to work with trapping horizons [ ent or dynamical horizon. There definitelycrosses is the a lower-left “Planck dashed horizon” line, or (which “reliability replacespersonal horizon”. the encounter notion Once with of one Planck event scale horizon), physics. onea is While spacelike guaranteed this singularity, a is the likely highly to curved be (highlyno just fluctuating, longer as highly an fatal discrete) as absolute shaded running region barrier into chronology is to now horizons unitary and evolution. the (Related “chronology protection ideas conjecture” have [ also arisen in the study of Black holes in general relativity p h k t r 4 l o s l r r i d t n i e e e r s s m a m s t f a s c a e t e 3 ff e r s a ( : : : : : . o e c r h s p ) ) n f a u e r i h e e d ’ m d o x s a t t g t d s c n l c n l m ( f t o o t i r m v h i h e m m a e o e n ) ) ) ) ) u n a s e v w n b a fi i z v , u a t f s o r u i i c n s F d i a f o , T p fl t c t s o , h t r y s o m c o u i ( o r h e v = h s v y v c r v ∞ e a t p d n n l t e i e O l u i y t b u o e q , . o , , , , y p v t e h e n v r a T d t r v o fi c u t e d b h b c u a n i ( n d h i t r f ( g l r e m . a e m a b n s c t e o a v i v . a t o , r v v a m t ∞ o G s v a e s c t o s , n r e h r e ( o t ( o i i g h ( h ( v y e ∈ u o s s ∈ p a y t e f b t n e o l v t l p − . e n t o l h n d t n i i i e l b o e a i ( a r h t ∈ ∈ e i e h e o s l ∈ m t m a n i ∈ a e / i h m g a s t v t h r m r e v v s - p v w t a h g a y o c i d v n t v s r f f ∈ v , o a i i s ∃ v h d y f , f ∃ p a t m g h i m A n l d u a , e T o o t a ∀ v t ∀ c o d r i ∀ i a g ∀ o s o a i e i

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n n o v a u c i h d i c T a c fl T e m b p I c m a e c v l e w p PoS(BHs, GR and Strings)001 ], where 0 on the Matt Visser 32 = r ]. I should caution the 33 7 . Furthermore, although Roman and Bergmann adopted are to a large extent compatible with each other, and both 3 4 and 3 is close to Schwarzschild and/or Kerr over a suitably large portion of Roman–Bergmann double-null causal diagram for a regular collapsing star. geometry is timelike, and with a suitable choice of coordinates can be “straightened out” so 5 Figure 5: There is also some very nice considerably older work by Roman and Bergmann [ These ideas have now mutated and spread throughout the theoretical relativity community, and they considered the possibilitythey of were obtaining not specifically apparent interested horizons incollapse without Hawking with radiation, an being a event more regular interested horizon. centre, inHayward many ideas and While of of Ashtekar–Bojowald stellar the causal qualitative diagrams. features of In that particular, article the now curve resonate labelled in the reader that just sketching a suitablePenrose causal diagram diagrams is only only capture the first thethink step, conformal since very structure by carefully definition of Carter– about thethat spacetime. the the metrical spacetime One structure should in — addition and one should fix the conformal factor so variants of these ideas can be seen, for instance, in recent work by Nielsen [ that it looks like the verticaldouble line null in figure coordinates to clarify thetransformation causal that structure, they is did needed not toa perform the pull Carter–Penrose singular asymptotic diagram. conformal infinity Not inan performing advantage; to this it a can singular finite make conformal “distance” thefeatures, transformation and (as diagram is opposed a so to little sometimes produce causal more features). realistic when it comes to studying the metric left of figure are compatible with the unitarydoes not evolution depend and on evaporation whether you of choosetheory black to of believe holes. “quantum in loops gravity” This or that strings, has qualitative or Einstein result indeed gravity any as other an candidate approximate low-energy limit. Black holes in general relativity no attempt has been madethe to two causal identify diagrams the of figures region of Planck-scale curvature. Despite appearances, PoS(BHs, GR and Strings)001 Matt Visser ], and many other 34 ]. 35 You do not need an event horizon to 8 you do not even need apparent/ dynamical/ trapping — asymptotic approach to trapping horizon formation is quite A long-lived apparent/ dynamical/ trapping horizon is more than sufficient. ]. This naturally leads one to ask: Do we actually need “black holes” to do “black Null geodesic expansion/contraction for a Roman–Bergmann regular collapsing star. 37 , 36 Can one avoid black hole formation with a suitably weirdCan equation one of avoid state? black hole formation with semi-classical quantum effects? Can one avoid black hole formation with “quantum gravity”? Figure 6: A key aspect of all these discussions is this critical point: More recently it has been realised that • • • workers of that period. Thisrepeatedly is forgotten, one and of repeatedly those rediscovered, elementary over and the utterly last 30 important years results [ that has been hole physics”? 4. Black hole mimics? Even if we do notthat actually we need have “black something holes” very to similar to do a “black black hole hole, physics”, a can “black we hole mimic”? at least be sure The possibilities are ratherfringe, tightly but constrained. names will (There be istives suppressed to of to black course protect hole the the formation“physically utter guilty.) can reasonable”.) gibbering be This The crackpot limited counted “physically set on reasonable” of the alternatives alterna- includes: fingers of one hand. (For selected values of horizons to get a Hawking-like flux sufficient [ the manifold. Furthermore, one shouldself-consistent really quantum calculation then leading patch to the awould resulting Hawking-like one spacetime flux have geometry a near onto really spatial compelling a infinity. picture Only of then black hole collapse andget evaporation. Hawking radiation. This is (or should be) a well-known result, dating back (at least) to Hajicek [ Black holes in general relativity PoS(BHs, GR and Strings)001 ], 46 ]. 1 various Matt Visser 49 . ]. r / 48 m , 47 1 where the horizon ]. ], and reference [ 43 . 56 r / m ] for a survey.) 1.) variant [ ]. 55 . r 45 / ]. In the region 2 et al. m (something unexpected?) (4.1) 52 ]. See [ , → 54 ]. Anisotropic pressures then ariase from 51 , , of “spacetimes”. (And none of the individual 41 ]. 45 50 ]? , 40 53 44 9 ]? 9 for any isotropic pressure profile. So you cannot / 43 8 ], and Laughlin neutron star ]: ≤ 42 ], and Amati variant [ ]. Typically the configuration is continually and asymp- → r 40 / The idea here is to change the equation of state of nuclear , 44 superposition ], and other proposals similar in spirit [ 48 ]. See also [ m , 39 46 , Here the idea is to have some nonsingular configuration that 43 47 ], strange stars [ , ]; 38 39 42 49 variant [ white dwarf → et al. ], see also [ 1, which is a signal that you are “close” to forming an apparent/ dynamical/ ]. 46 ], Q-balls [ . 41 38 r / The idea here is to have a (classical or possibly semiclassical) scalar field con- m These are hypothetical objects where the core is de Sitter like, and the exterior is Explicit calculations appear to be limited to the extremal/ near-extremal regime. The Ordinary star Breakdown of the spacetime manifold [ Quantum effects from the one-loop action [ Boson-stars [ Fuzz-balls: Mathur Dark stars/ Quasi-black holes [ Guaranteed anisotropies [ Quark stars [ Gravastars: Mazur–Mottola variant [ spacetime, rather it is taken to be a • • • • • • • • a Dark stars/ Quasi-black holes: for more details on the specific proposal by the current author and his collaborators.) Fuzz balls: black hole “interior” is replaced bynot “strongly interacting string muck”. The black“spacetimes” hole in “interior” the is superposition has a horizon [ Quark stars, Q-balls, strange stars: matter under extreme conditions [ The justification for the hypothesisedstill equation has the of Buchdahl–Bondi state bound: is 2 somewhat questionable. Note that one authors have argued for: mimics a black hole [ totically collapsing, but never quite developingeffects a horizon. as Typically an the intrinsic authors part appeal to of quantum the picture. (See the accompanying article [ the fact that the scalaranisotropic Lagrangian, classical combined stress-energy with tensor. sphericalcertainly symmetry, (And need automatically in the leads view anisotropies to if of an you the want Buchdahl–Bondi to get bound, “close” you to will 2 trapping horizon, unless you are at the very least willing to adopt anisotropic stresses [ figuration corresponding to a heavy compact object [ Black holes in general relativity get “close” to 2 Boson stars: Gravastars: would otherwise have formed [ Schwarzschild like, and something odd has to happen in the region 2 PoS(BHs, GR and Strings)001 . , . r t s t e e e k g o y y k y n n h s i s y t l i o a s c n g c t h l ! n n p o l e e l h i l i r a e t l l a h a t F a o a s a l r t l a c t a i o o T w r e s t l b w r . e t b o t m l h h t s M t Matt Visser e e . t n y n o a – G c R a a y n e r e e s N k k h 4 t n a w h t t e s e s h o i i f c s c t / o s e r . n i e g t n e a v a a k e s e g h s l a u l a h A h a s c e e e t e t m v h t d r b b l e r l s o a r s c t e n i l g n t o i d o e = l e o e a e a o b h a e c h l p v o h n h t g k g i t i r M t a s s n c e i s r f , r . i g i n m d c . (If one insists on an k e i a k s s i a . o B d s i . x w e o c l c s r e e t 2 p h s s n s m s o S i g i s a t e a c s y l x e g i e s l r o l 2 s t d n t l e , , a r e n e M i i n o b p . true. Two closely related, l b l p a a t r x a i 1 f a u y e e v d t 2 3 r c e o o e a = o e t t f t d s a ∼ r − − g a h d t n i s h h c d d w o h i r n r y i t s D D p t n p v c e t ! k a i a g t s b i d j r y w a e n r s i g y t e e e o y n r p n u e e r a B s h M n r n s d f c h h a h d e g t o i o r t h o i p M e e t almost t S t t c ! c l a e u t d ; e o ) t p s s f i ∼ s t t f ) t s y d n s α h 1 o e g o m n s s s v 1(b) o e d t e o e b t k o i n u c i r g o n o o u i e ( n g √ g s i y r h h u c r r t c v o t ]. There are also constraints coming h s n a i r B g t o t c p a i " a e n p a o T i l t r r b u S r o ∼ i s y h a m 57 c w s n t r t u m s g h t i a g e s m y u i t . f t l r i c a l ( o l u s e n . R e e g q l g o t ’ n o o m a h h a t r o n d l g w f l m e o i t n n i N t l h o n l t f n n o u n i o s t n i u e r , i o a ; e t a o n r i o i u i e e t c r n h s k t i L p t c g b i c r s u o s e e w c n i t r e s n m z e p y e s r c o r g N a a k s e g p d i t e h z ffi r s t e a l c r h s o s e a t u n r d h o u u t n o 3 e b a e s s m i a s f p 10 n t n q s l e g i f i l g t r f o i ‘ v t e o i o i a fi o o h a d p Fuzzball picture. n o f s r e h c r t t k i r t e h a g n r f o u a o c n w t a e t p c s n T p f h e n n o o o o s l e i o n c i p w e f t t o u c B y r c l e e . t i s o s a h e e c i e a r r i i s t c t v i p m r m u r e t p h s d t g s e o c y t e a u e u s o M u t h d u . Note however, that it is t l h c e e l a n a a e c x m e t o t e h o t i f r o n t u o h r e t l i r r I c ]. o c d h s m s t p m o m i d e a t m d c e h o g Figure 7: e t i . a t o s o s e p t o t c t n d g n t r s n t 58 e i 2 r i u r false r l u n h r a l u o f a a n e o e n c g t o h h d l h e u i e o s p a e c l n r t t n h T x n t r i z h o 1(a) t n d i d a t ( n e i t h ; c n m t ∼ n s h o t 1 e h n r o s t o i p s i k e d o s i s g t ) y a t s s w o . y u d t r o i . e c + t 0 in flat Minkowski space where the Riemann tensor is zero, and r l G o n c o e a d h n e h y a i t e fi 3 n a w i h t e t p s e h h i s h o n s p M c ff t e a i t t ! s t g t t i e = d o h c v s a a o n a W i l n v r c r c u i a a g t e d h r α c e t e p r s n t e h a i a r a t t t p b r n h s b r e e i a o a . e e ff c √ a p n l e m a m r ] s s t a c t g t e p h h e t i e n e i o g t r o d 3 s t i a l W m n s p s [ e e g u r c h g i ∼ e e i n e o f y y a n W t e e . h q s u n k l e t a r c h d d o e ] o i d s n e d n n o a t l o T s l a i i w c d i v s m . i t i M a e n s l m e s c i a a f g N l y a ) o r u h N . [ e a n c u h n e r s r k s a r t a s a c t a l H r s t n s n o d o o e o s o g D ( s y e n l i i a a o e m a f v e z s c e t i w i r o C e g i : t A t p r o i d t h a r e n a d h s m g 1 n u t m = a t a r t t t a i o u s . w a n e i a f . b T u i e M r i h e n t s u w y i o e t o p 2 t i t w t o m g r n e i r k r a r r s p h / c r e e n . , statements are: f c e S N s c t n u 1 o v v c i e e e i u e i o e s a l l r g n e o m g w a “Horizons are not detectable with local physics”. Calculations are often somewhat less explicittions than are one technically would difficult. like, simply because computa- There are a numbermimics of typically observational exhibit issues an to ergoregion address. instability [ For instance, rotating black hole from accretion observations [ “Event horizons are sometimes not detectable with local physics”; “Apparent/ dynamical/ trapping horizons are not detectable with ultra-local physics”. − v r f S r h h e i ! m i u o r o e u o r o o u h e t r n f Regarding the first point, it is an elementary exercise to verify that event horizons can form S α d c F i 2 S t r c q h c T p n T s f g i h d a true • • • • • The above statement is, of course, In short, one doesalong not any have one of complete the freedomobservational lines constraints. to described speculate, above should any at model some for stage be a carefully black confronted hole with the 5. mimic Detecting horizons? A common statement that one often encounters in the literature is this: For all of these black hole mimics, there are substantial issues to address: in locally flat portions ofpressure). Minkowski Apply spacetime. Birkhoff’s theorem. Just The let region aspacetime. outside dust the shell shell The is collapse region a (classical portion inside(and dust, of the the zero I Schwarzschild shell really is do a meanhorizons) portion event first of horizon, forms Minkowski this spacetime. at statement is The not event true horizon for apparent/ dynamical/ trapping Black holes in general relativity but Note the very careful and precise phrasing of these two statements. then sweeps out to encounter the infalling dust shell just as it crosses PoS(BHs, GR and Strings)001 ) (5.4) Matt Visser ultra-local is measurable r / ) r ( m 1. Furthermore, at least (though not is measurable using local ≈ ; (5.1) r 3 ) / r t ) / p local ] (see especially pages 27–28, r ) (which is related to the average 2 ( r 3 18 ( m r + the density. Now the stress-energy m r / ) p ρ r ( ; (5.2) − ; (5.3) r m ρ p ( π πρ π 4 4 4 − + − . ) ) ) ) r r 3 3 r r ( ( r r 11 ( ( 3 3 strong (local) gravity. is measurable using r r m m m m itself is just the radius of curvature of the surface r 2 2 6= − − r / ) = = = = r ( ˆ ˆ ˆ ˆ r φ φ φ ˆ t ˆ ˆ m t r ˆ ˆ r θ ˆ ˆ ˆ t φ ˆ φ φ ˆ t ˆ r R ˆ θ R R detectable using local (though not ultra-local) physics. At the R the transverse pressure, and = = t ˆ ˆ θ θ are p ˆ t ˆ r Event horizon ˆ θ ˆ θ ˆ t ˆ r R R ). In fact, it is an easy exercise to check [ r that the spacetime is static, then event horizons are also Killing horizons and are is the radial pressure, a priori r In spherically symmetric spacetimes, restricting attention toThe spherically most symmetric horizons: physically interesting horizons,detectable using the local apparent/ (though dynamical/ not ultra-local) trapping physics. horizons, are p Combining these observations: In spherically symmetric spacetimes 2 Regarding the second point, spherically symmetric apparent/ dynamical/ trapping horizons in • density inside radius using local (though not ultra-local) physics, anddynamical/ so trapping the presence horizons of spherically symmetricrisk apparent/ of initiating tribal warfare: of spherical symmetry passing through(though the not ultra-local) point physics. of interest, and is again measurable using local physics. To see this, recall(Equivalently, that physics in with any finite-size finite-range laboratoryspherical interactions you symmetry is can the measure orthonormal sensitive components the to of Riemanndensity, the the tensor. radial Riemann Riemann and tensor transverse are tensor.) pressures, linear and combinations But the of quantity in 2 (though not ultra-local) physics. Finally, in spherical symmetry, the quantity 2 and page 110, exercise 1): Here tensor is certainly measurable using local physics, therefore 2 spherically symmetric spacetimes are typically associated with 2 Event horizons are statements about the globaldistorted geometry, to even prevent if light the escaping global to geometry infinity,of is this sufficiently does the not tell gravitational you anything field aboutbecause at the they local occur the strength in event flat Minkowski horizonlocal space, itself. physics. are certainly not (If In detectable oneknows particular, (even in has this principle) additional by class any “metadata” ofalso this event apparent/ situation horizons, dynamical/ can trapping change. horizons —then as make For them we instance, detectable shall using if soon local see, one (though this not additional ultra-local) structure physics.) may Black holes in general relativity explicit calculation, then it is advisable tocoordinates.) use nonsingular The coordinates, key such point as is Painlevé–Gullstrand this: PoS(BHs, GR and Strings)001 , ]. 1 , ]. 1 Matt Visser (2003) L99 ]. 1 Theory of Black Hole 343 , (2008) 9. , arXiv:astro-ph/0510348. 1059 (2006) 1451 369 , arXiv:0706.1109 [gr-qc]. Published in [ The Kerr spacetime: Rotating black holes in , arXiv:0706.0622 [gr-qc]. Published in [ , AIP Conf. Proc. , Mon. Not. Roy. Astron. Soc. 12 Advection-Dominated Accretion around Black Holes ]. ]. Jet-dominated states: an alternative to advection across black ]. 1 3 Jet-dominated advective systems: radio and X-ray luminosity 59 , arXiv:0705.1537 [astro-ph]. Published in [ Advection-Dominated Accretion and the Black Hole Event Horizon , Mon. Not. Roy. Astron. Soc. The X-ray spectra of accreting Kerr black holes (2008) 733 [arXiv:0803.0322 [astro-ph]]. Cosmological Flashes from Rotating Black Holes 51 , Cambridge University Press, 2009. , Cambridge University Press, 1998. ]. 1 Rotating black holes and the Kerr metric Discovering the Kerr and Kerr-Schild metrics The Kerr spacetime: A brief introduction Supermassive Black Holes “Take the red pill to remain in denial. The blue pill to accept the bleak reality...” arXiv:astro-ph/0507409. Published in [ Accretion Discs New Astron. Rev. hole event horizons in ‘quiescent’ X-ray binaries [arXiv:astro-ph/0603731]. R. P. Kerr, dependence on the accretion rate general relativity arXiv:astro-ph/9803141. Published in [ [arXiv:astro-ph/0306614]. Published in [ I wish to thank Carlos Barceló, Veronika Hubeny, Stefano Liberati, José Senovilla, and Sebas- The message that I hope readers take from this micro-survey is that there are still many subtle [4] R. Narayan, R. Mahadevan and E. Quataert, [6] R. P. Fender, E. Gallo and P. G. Jonker, [3] Marek A. Abramowicz, Gunnlaugur Bjvrnsson, and James E. Pringle (editors), [5] R. Narayan and J. E. McClintock, [9] M. H. P. van Putten, [1] David Wiltshire, Matt Visser, and Susan Scott (editors), [7] E. Kording, R. Fender and S. Migliari, [8] F. Melia, [2] A. C. Fabian and G. Miniutti, [10] M. Visser, [11] R. P. Kerr, tiano Sonego for their comments and feedback. References Acknowledments and interesting things going on in blackat hole least physics. 50 Many years, deep issues and of by principleit some remain, is measure despite worthwhile 90 years, to work carefully onin re-analyze the my and subject. more re-assess Note cynical work also moments, from that I several in feel decades many that cases ago. each step Sometimes, forward involves 99% of a step backwards: 6. Discussion Black holes in general relativity When one moves beyond sphericalfaces symmetry, and/or either world of tubes the used spacetimebecomes to itself considerably define or more apparent/ of complex dynamical/ the [ trapping trapped horizons, sur- then the situation PoS(BHs, GR and Strings)001 (2006) (2004) (2000) (2006) 74 70 Matt Visser Test-beds 17 23 (2003) , Class. 68 , Living Rev. (2004) 251101 , Living Rev. Rel. , Adv. Theor. Math. 93 ]. ]. , Benjamin Cummings, 1 1 , Phys. Rev. D , Phys. Rev. D , Cambridge University , Phys. Rev. D (1994) 6467. (2007) 77. , Benjamin Cummings, 2003. , Class. Quant. Grav. 49 , Class. Quant. Grav. 69 , Imperial College Press, London, , Phys. Rev. Lett. . Published in [ . Published in [ Gravitation theory and gravitational , AIP Press [now Springer-Verlag], New Numerical Relativity , Freeman, San Francisco, 1973. 1 , arXiv:gr-qc/9303006. + , Pramana 3 , Phys. Rev. D No observational proof of the black-hole Gravitation 13 , arXiv:gr-qc/0008071. , arXiv:0810.0923 [gr-qc]. (2002) L31 [arXiv:astro-ph/0207270]. 396 The Large Scale Structure of Space-Time Modelling black hole evaporation Some uniqueness results for dynamical horizons , University of Chicago Press, 1984. Dynamical horizons: Energy, angular momentum, fluxes and balance Dynamical horizons and their properties Isolated and dynamical horizons and their applications (2002) 261101 [arXiv:gr-qc/0207080]. 89 (1998) 3147 [arXiv:gr-qc/9710089]. Energy and entropy conservation for dynamical black holes Angular momentum conservation for dynamical black holes Gravitational radiation from dynamical black holes Energy conservation for dynamical black holes Black holes: New horizons Unified first law of black-hole dynamics and relativistic thermodynamics General laws of black hole dynamics Marginal surfaces and apparent horizons Dynamics of black holes Spacetime and Geometry: An Introduction to General Relativity Event and Apparent Horizon Finders for Four decades of black holes uniqueness theorems , Astron. Astrophys. 15 Black Hole Dynamics In General Relativity General relativity Gravity: An Introduction to Einstein’s General Relativity Lorentzian wormholes: From Einstein to Hawking Global and local problems solved by the Kerr metric , University of Chicago Press, 1965. (2005) 1 [arXiv:gr-qc/0503109]. (2004) 10 [arXiv:gr-qc/0407042]. 9 7 , Phys. Rev. Lett. (2007) 3 [arXiv:gr-qc/0512169]. A. Ashtekar, R. M. Wald, J. B. Hartle, S. M. Carroll, 2003. collapse 2005. York, 1995. laws Phys. S. A. Hayward, 104027 [arXiv:gr-qc/0408008]. S. A. Hayward, 104013 [arXiv:gr-qc/0609008]. S. A. Hayward, L15 [arXiv:gr-qc/0505080]. S. A. Hayward, [arXiv:gr-qc/0404077]. S. A. Hayward, S. A. Hayward, Quant. Grav. S. A. Hayward, S. A. Hayward, event-horizon A. Ashtekar and B. Krishnan, Press, 1973. C. W. Misner, K. S. Thorne, and J. A. Wheeler, 104030 [arXiv:gr-qc/0308033]. A. Ashtekar and B. Krishnan, Rel. A. Ashtekar and G. J. Galloway, and applications for apparent horizon finders in numerical relativity 10 2159 [arXiv:gr-qc/9809004]. [13] D. Robinson, [15] B. K. Harrison, K. S. Thorne, M. Wakano, and J. A. Wheeler, [18] M. Visser, [19] A. Ashtekar and B. Krishnan, Black holes in general relativity [12] B. Carter, [14] S. W. Hawking and G. F. R. Ellis, [16] M. A. Abramowicz, W. Kluzniak and J. P. Lasota, [20] S. A. Hayward, [17] A. Fabbri and J. Navarros–Salas, [21] J. Thornburg, [22] M. Alcubierre, S. Brandt, B. Bruegmann, C. Gundlach, J. Masso, E. Seidel and P. Walker, PoS(BHs, GR and Strings)001 23 (2005) (1983) , 649 Matt Visser 22 28 12 , Int. J. Mod. (2006) 031103 The future of 96 , arXiv:0809.3850 (2008) 085010 , Nucl. Phys. Proc. Implementing an , In: 25 , arXiv:gr-qc/9412058. (1986) 309. , Phys. Rev. D (1992) 603. , Class. Quant. Grav. 182 46 , Class. Quant. Grav. (2005) 084013 , Int. J. Mod. Phys. D , Phys. Rev. Lett. (1987) 1065. 72 The future of theoretical physics and (1996) 4849 [arXiv:gr-qc/9606010]. 36 , arXiv:gr-qc/0504037. 54 , In: , Class. Quant. Grav. , Phys. Lett. B , Phys. Rev. D (1997) 8 [arXiv:gr-qc/9702041]. , arXiv:0802.3422 [gr-qc]. 415 , Phys. Rev. D A 3-D apparent horizon finder , Phys. Rev. D 14 , arXiv:0809.1711 [gr-qc]. , arXiv:0711.0313 [gr-qc]. , Phys. Rev. D , Phys. Lett. B Stellar Collapse Without Singularities? , Edited by: Gary Gibbons, Stuart Rankine; Paul Shellard. See , Proceedings of the Eighth Marcel Grossmann Meeting on General Spherically symmetric trapping horizons, the Misner-Sharp mass and Black hole evaporation: A paradigm Dynamical surface gravity Production and decay of evolving horizons Singularity avoidance by collapsing shells in quantum gravity , arXiv:0804.4435 [gr-qc]. Information Loss in Black Holes The Chronology Protection Conjecture Chronology Protection: Making The World Safe For Historians Formation and evaporation of regular black holes The disinformation problem for black holes Black holes and black hole thermodynamics without event horizons Black holes without boundaries Black Holes without Event Horizons Black holes as local horizons (2001) 775 [arXiv:gr-qc/0107102]. What simplified models say about unitarity and gravitational collapse On the origin of Hawking radiation Classical horizons and quantum corrections The quantum physics of chronology protection The reliability horizon Essential and inessential features of Hawking radiation The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often , Edited by: Gary Gibbons, Stuart Rankine; Paul Shellard. See pages 161–176. (2000) 114 [arXiv:gr-qc/9912064]. 10 88 apparent-horizon finder in three dimensions T. W. Baumgarte, G. B. Cook, M. A. Scheel, S. L. Shapiro and S. A. Teukolsky, J. Libson, J. Masso, E. Seidel and W. M. Suen, [arXiv:hep-th/0507171]. Suppl. Relativity; Jerusalem, June 1997, edited by:608-610. Tsvi [arXiv:gr-qc/9710020.] Piran, (World Scientific, Singapore, 1999), pages cosmology [arXiv:gr-qc/0204022]. S. W. Hawking, (2003) [arXiv:hep-th/0106111]. more important than back-reaction A. B. Nielsen and J. H. Yoon, A. B. Nielsen and M. Visser, A. B. Nielsen, 3349 [arXiv:gr-qc/0504029]. theoretical physics and cosmology pages 87–108. Phys. D [arXiv:gr-qc/0506126]. S. A. Hayward, 1265. [hep-th]. A. B. Nielsen, A. B. Nielsen and D. H.black Yeom, hole evaporation [arXiv:0711.1445 [gr-qc]]. A. B. Nielsen, (2006) 4637 [arXiv:gr-qc/0510083]. P. Hajicek, Black holes in general relativity [23] S. W. Hawking, [25] A. Ashtekar and M. Bojowald, [24] P. Hajicek, [28] M. Visser, [29] S. W. Hawking, [27] M. Visser, [32] T. A. Roman and P. G. Bergmann, [35] M. Visser, [26] M. Visser, [30] P. Hajicek and C. Kiefer, [31] S. A. Hayward, [33] A. B. Nielsen, [34] P. Hajicek, PoS(BHs, GR and Strings)001 , , 25 (2004) (2005) , 101 53 Matt Visser (1986) 121. , Class. Quant. 160 , arXiv:0810.4525 (1978) 1109. , Class. Quant. Grav. 17 (1986) 744]. , Fortsch. Phys. 269 (2002) 996 , Proc. Nat. Acad. Sci. (1986) 261. Is SAX J1808.4-3658 a strange (2003) 3587 [arXiv:gr-qc/0012094]. 572 310 , Astron. Astrophys. , Phys. Rev. D 18 Quantum phase transitions and the (2003) 831 [arXiv:gr-qc/0302028]. (2008) 609 [arXiv:hep-th/0612061]. 18 737 , Astrophys. J. Hawking-like radiation does not require a trapped , Astrophys. J. 15 (1985) 263 [Erratum-ibid. B , arXiv:0805.3716 [hep-th]. Boson stars: Gravitational equilibria of self-interacting Strange Quark Stars , Int. J. Mod. Phys. A 262 (1992) 163. (2002) 211303 [arXiv:hep-th/0202072]. Radiation from the non-extremal fuzzball Pair creation in non-extremal fuzzball geometries , Lect. Notes Phys. , Int. J. Mod. Phys. A 88 Strange stars Quark Star Phenomenology 220 (1986) 2485. 57 Dark energy and condensate stars: Casimir energy in the large Dark energy and condensate stars: A quantum alternative to classical Gravitational condensate stars: An alternative to black holes” Gravitational vacuum condensate stars Fuzzball geometries and higher derivative corrections for extremal holes Statistical interpretation of Bekenstein entropy for systems with a (2006) 171301 [arXiv:gr-qc/0607008]. (1999) 3776 [arXiv:hep-ph/9905356]. 97 , Nucl. Phys. B (2006) 5341 [arXiv:gr-qc/0604058]. 83 , Phys. Rept. , World Scientific, Singapore, 2006. 23 (2006) 48 [arXiv:hep-th/0412133]. Is RXJ1856.5-3754 a quark star? , Phys. Rev. Lett. , Emergent relativity Q Balls 738 The fuzzball proposal for black holes: An elementary review Fuzzballs and the information paradox: a summary and conjectures Tunneling into fuzzball states (2003) 31 [arXiv:gr-qc/0103073]. Proceedings of the 10th Marcel Grossmann Meeting (MG X 2003), Rio de Janeiro, Part , Phys. Rev. Lett. , et al. 29 The information paradox How strings solve the apparent contradiction between black holes and quantum coherence Boson stars (2008) 225021 [arXiv:0806.2309 [hep-th]]. , Phys. Rev. Lett. 25 , Phys. Rev. Lett. B. D. Chowdhury and S. D. Mathur, S. D. Mathur, R. B. Laughlin, 793 [arXiv:hep-th/0502050]. S. D. Mathur, [hep-th]. S. Giusto and S. D. Mathur, Nucl. Phys. B (2008) 135005 [arXiv:0711.4817 [hep-th]]. B. D. Chowdhury and S. D.Grav. Mathur, O. Lunin and S. D. Mathur, stretched horizon D. Amati, P. Jetzer, 9545 [arXiv:gr-qc/0407075]. P. O. Mazur and E. Mottola, arXiv:gr-qc/0405111. P. O. Mazur and E. Mottola, black holes breakdown of classical general relativity J. Phys. G scalar fields B, pages 1041–1047 P. O. Mazur and E. Mottola, arXiv:gr-qc/0109035. Class. Quant. Grav. region J. J. Drake [arXiv:astro-ph/0204159]. P. Haensel, J. L. Zdunik andX. R. D. Schaeffer, Li, I. Bombaci, M.star? Dey, J. Dey and E. P. J. van den Heuvel, [44] S. D. Mathur, [45] D. Amati, Black holes in general relativity [36] C. Barceló, S. Liberati, S. Sonego and M. Visser, [41] M. Colpi, S. L. Shapiro and I. Wasserman, [43] G. Chapline, E. Hohlfeld, R. B. Laughlin and D. I. Santiago, [37] C. Barceló, S. Liberati, S. Sonego and M. Visser, “Quasi-particle creation by analogue[38] black holes,” B. Freedman and L. D. McLerran, [42] P. O. Mazur and E. Mottola, [39] S. R. Coleman, [40] C. Alcock, E. Farhi and A. Olinto, PoS(BHs, GR and Strings)001 24 , , , Class. (2006) 74 , Phys. Matt Visser , Class. (2006) 013 , (2005) 4551 Effects of (2008) 117 (1999) 207 0602 22 , Class. Quant. Grav. , Class. Quant. Grav. 467 454 , Phys. Rev. D , Class. Quant. Grav. , JCAP , arXiv:0711.0006 [gr-qc]. (1976) 2169. 13 (2007) 024023 , Phys. Rept. , Phys. Lett. B (2006) 1525 [arXiv:gr-qc/0508115]. 75 , Class. Quant. Grav. 23 , Phys. Rev. D (2007) 124028 [arXiv:0707.3751 [gr-qc]]. Fate of gravitational collapse in semiclassical Small, dark, and heavy: But is it a black hole? Ergoregion instability of ultracompact astrophysical Ergoregion instability of black hole mimickers Instability of hyper-compact Kerr-like objects , Phys. Rev. D 16 76 Observation of Incipient Black Holes and the (2007) 024005 [arXiv:gr-qc/0609024]. Towards an S-matrix Description of Gravitational Stress Tensor from the Trace Anomaly in Born-Infeld Phantom Gravastars 76 , Class. Quant. Grav. Gravastars supported by nonlinear electrodynamics Gravastars must have anisotropic pressures How to tell a gravastar from a black hole Quantum Radiation from Quantum Gravitational Collapse , Phys. Rev. D Stable gravastars - an alternative to black holes? The fuzzball proposal for black holes Fundamental strings as black bodies , Phys. Rev. D Macroscopic effects of the quantum trace anomaly (2008) 124044 [arXiv:0709.0532 [gr-qc]]. (2008) 044032 [arXiv:0712.1130 [gr-qc]]. (2008) 049 [arXiv:0712.1209 [hep-th]]. 77 77 Hawking radiation and thin shells Stable gravastars with generalised exteriors (2008) 195010 [arXiv:0808.1615 [gr-qc]]. (2007) 1069 [arXiv:gr-qc/0611083]. 0802 Schrodinger Picture of Quantum Gravitational Collapse Stable dark energy stars Van der Waals quintessence stars 25 24 (2008) 107 [arXiv:gr-qc/0701096]. , JHEP 663 , Phys. Rev. D , Phys. Rev. D (2005) 4189 [arXiv:gr-qc/0505137]. (2004) 1135 [arXiv:gr-qc/0310107]. gravity T. Vachaspati and D. Stojkovic, Lett. B T. Vachaspati, D. Stojkovic and L. M. Krauss, Information Loss Problem B. M. N. Carter, 22 21 Proceedings of Science, accompanying article in this volume. objects V. Cardoso, P. Pani, M. Cadoni and M. Cavaglia, [arXiv:gr-qc/0509087]. N. Bilic, G. B. Tupper and[arXiv:astro-ph/0503427]. R. D. Viollier, [arXiv:0804.0552 [hep-th]]. Quant. Grav. P. Pani, V. Cardoso, M. Cadoni andarXiv:0901.0850 M. [gr-qc]. Cavaglia, F. S. N. Lobo and A. V. B. Arellano, Quant. Grav. F. S. N. Lobo, [arXiv:hep-th/9901092]. Reissner-Nordstrom Spacetimes Collapse D. Amati and J. G. Russo, [arXiv:gr-qc/0610118]. (2007) 4191 [arXiv:0706.1513 [gr-qc]]. quantized fields on the spacetime geometriesarXiv:0709.4457 of [gr-qc]. static spherically symmetric blackP. holes R. Anderson, E. Mottola and R. Vaulin, E. Mottola and R. Vaulin, 064004 [arXiv:gr-qc/0604051]. Black holes in general relativity [46] C. Barceló, S. Liberati, S. Sonego and M. Visser, [48] T. Vachaspati, [47] D. G. Boulware, [49] C. Cattoen, T. Faber and M. Visser, [50] M. Visser and D. L. Wiltshire, [57] V. Cardoso, P. Pani, M. Cadoni and M. Cavaglia, [51] F. S. N. Lobo, [56] C. Barceló, S. Liberati, S. Sonego and M. Visser, [55] K. Skenderis and M. Taylor, [52] C. B. M. Chirenti and L. Rezzolla, [53] P. R. Anderson, M. Binkley, H. Calderon, W. A. Hiscock, E. Mottola and R. Vaulin, [54] D. Amati, M. Ciafaloni and G. Veneziano, PoS(BHs, GR and Strings)001 79 Matt Visser , Phys. Rev. , Phys. Rev. D , arXiv:0812.2767 17 (2007) 659 [arXiv:gr-qc/0701154]. 24 A Note on trapped Surfaces in the Vaidya Solution On the ergoregion instability in rotating gravastars Where are all the gravastars? Limits upon the gravastar model from , Class. Quant. Grav. On the boundary of the region containing trapped surfaces (2008) 084011 [arXiv:0808.4080 [gr-qc]]. accreting black holes 78 (2009) 024027. [arXiv:0809.2213 [gr-qc]]. J. M. M. Senovilla, [gr-qc]. C. B. M. Chirenti and L. Rezzolla, [58] A. E. Broderick and R. Narayan, [59] I. Bengtsson and J. M. M. Senovilla, Black holes in general relativity