The VECRO hypothesis Samir D. Mathur The Ohio State University Thanks to everyone for making possible this wonderful conference in these difficult circumstances (arxiv: 1703.03042,1705.06407, 1812.11641, 1905.12004, 2001.11057) The black hole information paradox total ,total n n ,total n n ,total n n total entanglement − 1 5 − 1 5 − 1 5 black n = (J (2n 2)) (J (2n 4)) . .to(talJ 2 ) ,total 1 n1n5 ,total n1n5(5) ,total n1n5 total | ⇧ − − − − n −= (J −(2n 2)| )⇧ (J −(2n 4)) . (J −2 ) 1 (5) | ⇧ − − − − − | ⇧ hole A = S = 2⇥⌥n1n2n3 A 4G = S = 2⇥⌥n1n2n3 4G normal 1 1 2 ∆E = + = 1 1 1 2 body nR nR nR ∆E (=0 0 + 1 1=)+O(✏) p | in|Ri nR| i| i nR 2 2 ∆E = 2 nR ∆E = time nR S = ln(1) = 0 (6) Fuzzballs: Consider bound statesS = ln(1) of branes= 0 in string theory: (6) S = 2⌥2⇥⌥n1n2 (7) S = 2⌥2⇥⌥n1n2 (7) S = 2⇥⌥n1n2n3 (8) weak coupling Sstrong= 2⇥⌥ ncoupling1n2n3 (8) S = 2⇥⌥n1n2n3n4 (9) S = 2⇥⌥n1n2n3n4 (9) n1 n5 n ⇤ ⇤ n1 n5 n 1 ⇤ ⇤ n 4 lp 1 ⇤ n 4 lp 1 ⇤ n 2 lp 1 ⇤ n 2 lp The size of the bound state grows ⇤ n lp with the number of branes, and a ⇤ n lp 1 ⇤ M9,1 M4,1 K3 S 1 horizon never forms ⌅ ⇥ ⇥ M9,1 M4,1 K3 S A ⌅ ⇥ ⇥ n1n5 J S A fuzzball 4G ⇤ − ⇤ n1n5 J S 4G ⇤ − ⇤ A ⌥n1n5 S A 4G ⇤ ⇤ ⌥n1n5 S 4G ⇤ ⇤ e2π⇥2⇥n1np e2π⇥2⇥n1np Q1 1 + Q1 r2 1 + r2 Qp 1 + Qp r2 1 + r2 e2π⇥2⇥n1n5 e2π⇥2⇥n1n5 i(t+y) ikz w = e− − w˜(r, θ, ⇤) i(t+y) ikz (10) w = e− − w˜(r, θ, ⇤) (10) (2) i(t+y) ikz ˜(2) BMN = e− − BMN (r, θ, ⇤) , (2) i(t+y) ikz ˜(2)(11) BMN = e− − BMN (r, θ, ⇤) , (11) 2 2 In the fuzzball paradigm, black hole microstates do not have a horizon; they radiate like normal objects from their surface Thus we do not have any information puzzle But we will learn a lot by asking a more refined question: Where and why does the semiclassical approximation break down ? ?? ?? We will assume that there are no large violations of causality in our gravity theory No !! Then, how does the semiclassical collapse get replaced by fuzzball formation ? This is the central aspect of the paradox from the viewpoint of a relativist. (This is a qualitative question, so our discussion will also be qualitative) <latexit sha1_base64="bdyZiiy4M1NTbWgou2C8HXMXH2A=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoseCF49V7Ae0oWy2k3TpZhN3N0Ip/RNePCji1b/jzX/jts1BWx8MPN6bYWZekAqujet+O4W19Y3NreJ2aWd3b/+gfHjU0kmmGDZZIhLVCahGwSU2DTcCO6lCGgcC28HoZua3n1BpnsgHM07Rj2kkecgZNVbq3PeiiIh+2i9X3Ko7B1klXk4qkKPRL3/1BgnLYpSGCap113NT40+oMpwJnJZ6mcaUshGNsGuppDFqfzK/d0rOrDIgYaJsSUPm6u+JCY21HseB7YypGeplbyb+53UzE177Ey7TzKBki0VhJohJyOx5MuAKmRFjSyhT3N5K2JAqyoyNqGRD8JZfXiWti6pXq17e1Sr1Wh5HEU7gFM7Bgyuowy00oAkMBDzDK7w5j86L8+58LFoLTj5zDH/gfP4AiOSPmw==</latexit> <latexit sha1_base64="UMXJVd/S2E/lmUrul0BOPTYfUws=">AAAB+HicbVDJSgNBEO1xjXHJqEcvjUGIlzAjcTkGRPAYlywwGYaeTk3SpGehu0eMQ77EiwdFvPop3vwbO8kcNPFBweO9Kqrq+QlnUlnWt7G0vLK6tl7YKG5ube+UzN29loxTQaFJYx6Ljk8kcBZBUzHFoZMIIKHPoe0PLyd++wGEZHF0r0YJuCHpRyxglCgteWbp6jFx7rzMh+G4cnvsembZqlpT4EVi56SMcjQ886vbi2kaQqQoJ1I6tpUoNyNCMcphXOymEhJCh6QPjqYRCUG62fTwMT7SSg8HsdAVKTxVf09kJJRyFPq6MyRqIOe9ifif56QquHAzFiWpgojOFgUpxyrGkxRwjwmgio80IVQwfSumAyIIVTqrog7Bnn95kbROqnatenpTK9fP8jgK6AAdogqy0Tmqo2vUQE1EUYqe0St6M56MF+Pd+Ji1Lhn5zD76A+PzBwA9kqE=</latexit> We will argue for a picture of the quantum gravity vacuum which will resolve this puzzle We call this picture the VECRO hypothesis VECRO: Virtual Extended Compression-Resistant Objects (a) On shell microstates are Extended objects (fuzzballs) with size R 2GM + l ⇠ p (b) Thus the quantum gravity vacuum must contain Virtual fluctuations corresponding to these objects (c) The fluctuations to a fuzzball type configuration with R l will be highly p suppressed, but there are Exp [ S bek ( R )] fuzzball states of this size, so there will be a large phase space of such configurations. We assume that the largeness of this phase space will offset the suppression, so that these vecro fluctuations are an important component of the quantum gravity vacuum The VECRO hypothesis: The quantum gravity vacuum contains an important component consisting of virtual fuzzball type configurations. This component plays a crucial role in situations where a horizon is predicted by the semiclassical theory, and modifies the dynamics to resolve the puzzles that arise (a) Explains how a collapsing shell turns into fuzzballs while maintaining causality of the underlying theory (b) Gives a resolution of the bags of gold problem (c) Are the Rindler, Black hole, Cosmological horizons similar? (No, differ in vecro flictuations) (d) Can impact cosmological issues like inflation, cosmological constant, bubble nucleation Fuzzballs Avery, Balasubramanian, Bena, Bobev, Bossard, Carson, Ceplak, Chowdhury, de Boer, Gimon, Giusto, Guo, Hampton, Heidmann, Jejjala, Katmadas, Kanitscheider, Keski-Vakkuri, Kraus, Levi, Lunin, Madden, Maldacena, Maoz, Martinec, Mayerson, Niehoff, Park, Peet, Potvin, Puhm, Ross, Ruef, Rychkov, Saxena, Shigemori, Simon, Skenderis, Srivastava, Taylor, Titchner, Turton, Vasilakis, Wang, Warner ... and many others total ,total n1n5 ,total n1n5 ,total n1n5 total n = (J −(2n 2)) (J −(2n 4)) . (J −2 ) 1 (5) | ⇧ − − − − − | ⇧ total ,total n1n5 ,total n1n5 ,total n1n5 total n = (J −(2n 2)) (J −(2n 4)) . (J −2 ) 1 (5) A | ⇧ − − − − − | ⇧ = S = 2⇥⌥n n n 4G 1 2 3 A = S = 2⇥⌥n n n 4G 1 2 3 1 1 2 ∆E = + = 1 1 2 nR nR nR ∆E = + = 2 nR nR nR ∆E = 2 nR ∆E = S = ln(1) = 0 nR(6) Consider the bound states of D1,S = ln(1)D5, P= charges.0 (6) S = 2⌥2⇥⌥n1n2 (7) S = 2⌥2⇥⌥n1n2 (7) S =weak2⇥⌥n coupling1n2n3 strong coupling(8) S = 2⇥⌥n1n2n3 (8) S = 2⇥⌥n1n2n3n4 (9) S = 2⇥⌥n1n2n3n4 (9) n1 n5 n ⇤ ⇤ n1 n5 n 1 ⇤ ⇤ n 4 lp 1 ⇤ n 4 lp 1 ⇤ n 2 l 1 p n 2 l ⇤ ⇤ p n lp The size of the bound state grows ⇤ n lp 1 ⇤ with the number of branes, and a M9,1 M4,1 K3 S M M K3 S1 ⌅ ⇥ ⇥ 9,1 ⌅ 4,1 ⇥ ⇥ horizon never forms A A n1n5 J S n n J S 4G ⇤ − ⇤ 4G ⇤ 1 5 − ⇤ fuzzball A A ⌥n n S 1 1 5 2 4 ⌥3 n1n5 S 4G ⇤ ⇤ pn1n5np g 4↵G0 ⇤ ⇤ D RH (SDM hep-th/9706151) 2π⇥2 n n VL 2π⇥2 n n e ⇥ 1 p ⇠ " e# ⇥⇠1 p Q Q1 1 + 1 1 + Many examplesr2 of string solutions haver2 been constructed, and in each case we have found Qthat the solution has no horizonQ p(Large program by Bena, Warner et al) 1 + p 1 + r2 r2 (All 2 charge extremal states, many families of 3 and 4 charge extremal, some families of 2π⇥2⇥n1n5 nonextremal,e2π⇥2⇥n1n5 radiation from near eextremal matches expectations exactly …) i(t+y) ikz i(t+y) ikz w = e− − w˜(r, θ, ⇤) (10) w = e− − w˜(r, θ, ⇤) (10) (2) i(t+y) ikz ˜(2) (2) i(t+y) ikz ˜(2) BMN = e− − BMN (r, θ, ⇤) , (11) BMN = e− − BMN (r, θ, ⇤) , (11) 2 2 Fuzzball conjecture: No microstate in string theory will have a traditional horizon which has a vacuum region in its vicinity 1 ( 0 0 + 1 1 )+O(✏) state of radiated quantum depends p2 | i| i | i| i on details at the surface How did we bypass the various no-hair theorems? There are special features of a theory like string theory which has extra dimensions/ extended objects/Chern-Simmons terms etc. (Gibbons+Warner 13) What about Buchdahl theorem? Fluid sphere with pressure decreasing outwards must collapse if 9 R< M 4 Toy model: Euclidean Schwarzschild plus time (‘neutral fuzzball’) Hole cut out of space 2 2 2 r0 2 dr 2 2 2 2 ds = dt +(1 )d⌧ + + r (d✓ +sin ✓dφ ) , 0 ⌧ < 4⇡r0 − − r 1 r0 − r We can reduce on the direction ⌧ to get a scalar field in 3+1 gravity. 1 The stress tensor is the standard one for a scalar field T = Φ Φ gE Φ Φ,λ µ⌫ ,µ ,⌫ − 2 µ⌫ ,λ Why does this shell of scalar field not collapse inwards ? 2 µ 3r0 T ⌫ = diag ⇢,pr,p✓,pφ = diag f,f, f, f , f = r 3 {− } {− − − } 8r4(1 0 ) 2 − r Pressure diverges at tip of cigar so a Buchdahl type analysis would call this a singularity But the 4+1 dimensional solution is completely regular ( g tt never changes sign, so there is no horizon ) In general constructing a fuzzball needs all the details of string theory: extra dimensions, strings, branes, fluxes, … But for our present purposes we can keep in mind a heuristic picture of the fuzzball where we have many the holes (bubbles) in space that are linked together in a way that they support each other … The causality puzzle ?? ?? Shell passes through horizon Light cones point inwards Collapsing shell with all curvatures low inside horizon We will assume: If curvatures are low throughout a spacetime region, then causality holds to leading order. Here causality means that signals do not propagate outside the light cone, and that there are no nonlocal interactions between points that are spacelike separated. How do we form the fuzzball? No large effects ?? A strong constraint comes from considering partial shells <latexit sha1_base64="BKdRtGV3cHLHdJmQC3LiwYHf4YA=">AAAB73icbVBNSwMxEJ3Ur1q/qh69BIvgqexKRY8FLx6r2A9ol5JNs21okl2TrFCW/gkvHhTx6t/x5r8xbfegrQ8GHu/NMDMvTAQ31vO+UWFtfWNzq7hd2tnd2z8oHx61TJxqypo0FrHuhMQwwRVrWm4F6ySaERkK1g7HNzO//cS04bF6sJOEBZIMFY84JdZJnZ7hEt/3R/1yxat6c+BV4uekAjka/fJXbxDTVDJlqSDGdH0vsUFGtOVUsGmplxqWEDomQ9Z1VBHJTJDN753iM6cMcBRrV8riufp7IiPSmIkMXackdmSWvZn4n9dNbXQdZFwlqWWKLhZFqcA2xrPn8YBrRq2YOEKo5u5WTEdEE2pdRCUXgr/88ippXVT9WvXyrlap1/I4inACp3AOPlxBHW6hAU2gIOAZXuENPaIX9I4+Fq0FlM8cwx+gzx+UPo+i</latexit> Shell collapsing (a) black hole (b) Partial shell continues in; rest at speed of light formation stops; expect no black hole formation If we only consider small scale vacuum fluctuations we will be trapped by the causality problem Virtual fuzzballs of radius R can ‘feel Aichelburg-Sexl shock wave; vacuum ⇠ h fluctuations return to original form around’ the scale of the collapsing shell and know when a hole should form after wave Resolution of the causality puzzle under the VECRO hypothesis <latexit sha1_base64="Pm/QPTY8F7gwP44NgGfqtbN7ZvE=">AAAB8HicbVA9SwNBEJ2LXzF+RS1tFoNgFe5CgiksAjaWEcyHJGfY2+wlS3b3jt09IRz5FTYWitj6c+z8N26SKzTxwcDjvRlm5gUxZ9q47reT29jc2t7J7xb29g8Oj4rHJ20dJYrQFol4pLoB1pQzSVuGGU67saJYBJx2gsnN3O88UaVZJO/NNKa+wCPJQkawsdJDP2aDyWPl2h0US27ZXQCtEy8jJcjQHBS/+sOIJIJKQzjWuue5sfFTrAwjnM4K/UTTGJMJHtGepRILqv10cfAMXVhliMJI2ZIGLdTfEykWWk9FYDsFNmO96s3F/7xeYsK6nzIZJ4ZKslwUJhyZCM2/R0OmKDF8agkmitlbERljhYmxGRVsCN7qy+ukXSl71XLtrlpq1LM48nAG53AJHlxBA26hCS0gIOAZXuHNUc6L8+58LFtzTjZzCn/gfP4A6aWPzQ==</latexit>