Closed Timelike Curves and Causality Violation
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Dynamics of the Four Kinds of Trapping Horizons & Existence of Hawking
Dynamics of the four kinds of Trapping Horizons & Existence of Hawking Radiation Alexis Helou1 AstroParticule et Cosmologie, Universit´eParis Diderot, CNRS, CEA, Observatoire de Paris, Sorbonne Paris Cit´e Bˆatiment Condorcet, 10, rue Alice Domon et L´eonieDuquet, F-75205 Paris Cedex 13, France Abstract We work with the notion of apparent/trapping horizons for spherically symmetric, dynamical spacetimes: these are quasi-locally defined, simply based on the behaviour of congruence of light rays. We show that the sign of the dynamical Hayward-Kodama surface gravity is dictated by the in- ner/outer nature of the horizon. Using the tunneling method to compute Hawking Radiation, this surface gravity is then linked to a notion of temper- ature, up to a sign that is dictated by the future/past nature of the horizon. Therefore two sign effects are conspiring to give a positive temperature for the black hole case and the expanding cosmology, whereas the same quantity is negative for white holes and contracting cosmologies. This is consistent with the fact that, in the latter cases, the horizon does not act as a separating membrane, and Hawking emission should not occur. arXiv:1505.07371v1 [gr-qc] 27 May 2015 [email protected] Contents 1 Introduction 1 2 Foreword 2 3 Past Horizons: Retarded Eddington-Finkelstein metric 4 4 Future Horizons: Advanced Eddington-Finkelstein metric 10 5 Hawking Radiation from Tunneling 12 6 The four kinds of apparent/trapping horizons, and feasibility of Hawking radiation 14 6.1 Future-outer trapping horizon: black holes . 15 6.2 Past-inner trapping horizon: expanding cosmology . -
Summer 2017 Astron 9 Week 5 Final Version
RELATIVITY OF SPACE AND TIME IN POPULAR SCIENCE RICHARD ANANTUA PREDESTINATION (MON JUL 31) REVIEW OF JUL 24, 26 & 28 • Flying atomic clocks, muon decay, light bending around stars and gravitational waves provide experimental confirmation of relativity • In 1919, Einstein’s prediction for the deflection of starlight was confirmed by • The 1971 Hafele-Keating experiment confirmed • The 1977 CERN muon experiment confirmed • In 2016 LIGO confirmed the existence of REVIEW OF JUL 24, 26 & 28 • Flying atomic clocks, muon decay, light bending around stars and gravitational waves provide experimental confirmation of relativity • In 1919, Einstein’s prediction for the deflection of starlight was confirmed by Sir Arthur Eddington • The 1971 Hafele-Keating experiment confirmed motional and gravitational time dilation • The 1977 CERN muon experiment confirmed motional time dilation • In 2016 LIGO confirmed the existence of gravitational waves TIME TRAVEL IN RELATIVITY • Methods of time travel theoretically possible in relativity are • (Apparently) faster than light travel – window into the past? • Closed timelike curved • (Apparent) paradoxes with time travel • Kill your grandfather – past time travel may alter seemingly necessary conditions for the future time traveler to have started the journey • Predestination - apparent cause of past event is in the future SPECIAL RELATIVISTIC VELOCITY ADDITION • In special relativity, no object or information can travel faster than light, a fact reflected in the relativistic law of composition of velocities v &v vAB v = $% %' A !" v$%v%' (& * ) vBC B C • vAB is the (1D) velocity of A with respect to B • vBC is the (1D) velocity of B with respect to C POP QUIZ - FASTER THAN LIGHT TRAVEL • A spaceship traveling at v>c is returning from a moving planet (L0 away right before the journey). -
Closed Timelike Curves Make Quantum and Classical Computing Equivalent
Closed Timelike Curves Make Quantum and Classical Computing Equivalent Scott Aaronson∗ John Watrous† MIT University of Waterloo Abstract While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class PSPACE, consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves an open problem proposed by one of us in 2005, and gives an essentially complete understanding of computational complexity in the presence of CTCs. Following the work of Deutsch, we treat a CTC as simply a region of spacetime where a “causal consistency” condition is imposed, meaning that Nature has to produce a (probabilistic or quantum) fixed-point of some evolution operator. Our conclusion is then a consequence of the following theorem: given any quantum circuit (not necessarily unitary), a fixed-point of the circuit can be (implicitly) computed in polynomial space. This theorem might have independent applications in quantum information. 1 Introduction The possibility of closed timelike curves (CTCs) within general relativity and quantum gravity theories has been studied for almost a century [11, 15, 13]. A different line of research has sought to understand the implications of CTCs, supposing they existed, for quantum mechanics, computation, and information [9, 8, 5]. In this paper we contribute to the latter topic, by giving the first complete characterization of the computational power of CTCs. -
BLACK HOLES: the OTHER SIDE of INFINITY General Information
BLACK HOLES: THE OTHER SIDE OF INFINITY General Information Deep in the middle of our Milky Way galaxy lies an object made famous by science fiction—a supermassive black hole. Scientists have long speculated about the existence of black holes. German astronomer Karl Schwarzschild theorized that black holes form when massive stars collapse. The resulting gravity from this collapse would be so strong that the matter would become more and more dense. The gravity would eventually become so strong that nothing, not even radiation moving at the speed of light, could escape. Schwarzschild’s theories were predicted by Einstein and then borne out mathematically in 1939 by American astrophysicists Robert Oppenheimer and Hartland Snyder. WHAT EXACTLY IS A BLACK HOLE? First, it’s not really a hole! A black hole is an extremely massive concentration of matter, created when the largest stars collapse at the end of their lives. Astronomers theorize that a point with infinite density—called a singularity—lies at the center of black holes. SO WHY IS IT CALLED A HOLE? Albert Einstein’s 1915 General Theory of Relativity deals largely with the effects of gravity, and in essence predicts the existence of black holes and singularities. Einstein hypothesized that gravity is a direct result of mass distorting space. He argued that space behaves like an invisible fabric with an elastic quality. Celestial bodies interact with this “fabric” of space-time, appearing to create depressions termed “gravity wells” and drawing nearby objects into orbit around them. Based on this principle, the more massive a body is in space, the deeper the gravity well it will create. -
Closed Timelike Curves, Singularities and Causality: a Survey from Gödel to Chronological Protection
Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection Jean-Pierre Luminet Aix-Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille , France; Centre de Physique Théorique de Marseille (France) Observatoire de Paris, LUTH (France) [email protected] Abstract: I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to save the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role. Keywords: time travel; closed timelike curves; singularities; wormholes; Gödel’s universe; chronological protection; causal dynamical triangulations 1. Introduction In 1949, the mathematician and logician Kurt Gödel, who had previously demonstrated the incompleteness theorems that broke ground in logic, mathematics, and philosophy, became interested in the theory of general relativity of Albert Einstein, of which he became a close colleague at the Institute for Advanced Study at Princeton. -
Light Rays, Singularities, and All That
Light Rays, Singularities, and All That Edward Witten School of Natural Sciences, Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics at the Institute for Advanced Study, and also at the 2020 New Zealand Mathematical Research Institute summer school in Nelson, New Zealand. Contents 1 Introduction 3 2 Causal Paths 4 3 Globally Hyperbolic Spacetimes 11 3.1 Definition . 11 3.2 Some Properties of Globally Hyperbolic Spacetimes . 15 3.3 More On Compactness . 18 3.4 Cauchy Horizons . 21 3.5 Causality Conditions . 23 3.6 Maximal Extensions . 24 4 Geodesics and Focal Points 25 4.1 The Riemannian Case . 25 4.2 Lorentz Signature Analog . 28 4.3 Raychaudhuri’s Equation . 31 4.4 Hawking’s Big Bang Singularity Theorem . 35 5 Null Geodesics and Penrose’s Theorem 37 5.1 Promptness . 37 5.2 Promptness And Focal Points . 40 5.3 More On The Boundary Of The Future . 46 1 5.4 The Null Raychaudhuri Equation . 47 5.5 Trapped Surfaces . 52 5.6 Penrose’s Theorem . 54 6 Black Holes 58 6.1 Cosmic Censorship . 58 6.2 The Black Hole Region . 60 6.3 The Horizon And Its Generators . 63 7 Some Additional Topics 66 7.1 Topological Censorship . 67 7.2 The Averaged Null Energy Condition . -
Einstein's Gravitational Field
Einstein’s gravitational field Abstract: There exists some confusion, as evidenced in the literature, regarding the nature the gravitational field in Einstein’s General Theory of Relativity. It is argued here that this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with. 1 Author: Peter M. Brown e-mail: [email protected] 2 INTRODUCTION Einstein’s General Theory of Relativity (EGR) has been credited as the greatest intellectual achievement of the 20th Century. This accomplishment is reflected in Time Magazine’s December 31, 1999 issue 1, which declares Einstein the Person of the Century. Indeed, Einstein is often taken as the model of genius for his work in relativity. It is widely assumed that, according to Einstein’s general theory of relativity, gravitation is a curvature in space-time. There is a well- accepted definition of space-time curvature. As stated by Thorne 2 space-time curvature and tidal gravity are the same thing expressed in different languages, the former in the language of relativity, the later in the language of Newtonian gravity. However one of the main tenants of general relativity is the Principle of Equivalence: A uniform gravitational field is equivalent to a uniformly accelerating frame of reference. This implies that one can create a uniform gravitational field simply by changing one’s frame of reference from an inertial frame of reference to an accelerating frame, which is rather difficult idea to accept. -
Tippett 2017 Class. Quantum Grav
Citation for published version: Tippett, BK & Tsang, D 2017, 'Traversable acausal retrograde domains in spacetime', Classical Quantum Gravity, vol. 34, no. 9, 095006. https://doi.org/10.1088/1361-6382/aa6549 DOI: 10.1088/1361-6382/aa6549 Publication date: 2017 Document Version Peer reviewed version Link to publication Publisher Rights CC BY-NC-ND This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at: https://doi.org/10.1088/1361-6382/aa6549 University of Bath Alternative formats If you require this document in an alternative format, please contact: [email protected] General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 05. Oct. 2021 Classical and Quantum Gravity PAPER Related content - A time machine for free fall into the past Traversable acausal retrograde domains in Davide Fermi and Livio Pizzocchero - The generalized second law implies a spacetime quantum singularity theorem Aron C Wall To cite this article: Benjamin K Tippett and David Tsang 2017 Class. -
Stable Wormholes in the Background of an Exponential F (R) Gravity
universe Article Stable Wormholes in the Background of an Exponential f (R) Gravity Ghulam Mustafa 1, Ibrar Hussain 2,* and M. Farasat Shamir 3 1 Department of Mathematics, Shanghai University, Shanghai 200444, China; [email protected] 2 School of Electrical Engineering and Computer Science, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan 3 National University of Computer and Emerging Sciences, Lahore Campus, Punjab 54000, Pakistan; [email protected] * Correspondence: [email protected] Received: 21 January 2020; Accepted: 3 March 2020; Published: 26 March 2020 Abstract: The current paper is devoted to investigating wormhole solutions with an exponential gravity model in the background of f (R) theory. Spherically symmetric static spacetime geometry is chosen to explore wormhole solutions with anisotropic fluid source. The behavior of the traceless matter is studied by employing a particular equation of state to describe the important properties of the shape-function of the wormhole geometry. Furthermore, the energy conditions and stability analysis are done for two specific shape-functions. It is seen that the energy condition are to be violated for both of the shape-functions chosen here. It is concluded that our results are stable and realistic. Keywords: wormholes; stability; f (R) gravity; energy conditions 1. Introduction The discussion on wormhole geometry is a very hot subject among the investigators of the different modified theories of gravity. The concept of wormhole was first expressed by Flamm [1] in 1916. After 20 years, Einstein and Rosen [2] calculated the wormhole geometry in a specific background. In fact, it was the second attempt to realize the basic structure of wormholes. -
Quantum Time Machines Are Expectation Values of the Scalar field Squared and Stress- Quantum-Mechanically Stable
Quantum time machine Pedro F. Gonz´alez-D´ıaz Centro de F´ısica “Miguel Catal´an”, Instituto de Matem´aticas y F´ısica Fundamental, Consejo Superior de Investigaciones Cient´ıficas, Serrano 121, 28006 Madrid (SPAIN) (December 6, 1997) The continuation of Misner space into the Euclidean region is seen to imply the topological re- striction that the period of the closed spatial direction becomes time-dependent. This restriction results in a modified Lorentzian Misner space in which the renormalized stress-energy tensor for quantized complex massless scalar fields becomes regular everywhere, even on the chronology hori- zon. A quantum-mechanically stable time machine with just the sub-microscopic size may then be constructed out of the modified Misner space, for which the semiclassical Hawking’s chronology protection conjecture is no longer an obstruction. PACS number(s): 04.20.Gz, 04.62.+v I. INTRODUCTION some attempts intended to violate it [14,15], this con- jecture has survived rather forcefully [16]. However, the After the seminal papers by Morris, Thorne and Yurt- realm where chronology protection holds is semiclassical sever [1], the notion of a time machine has jumped from physics, as it is for all hitherto proposed time machines. the pages of science fiction books to those of scientific Actually, because spacetime foam [17] must entail strong journals, giving rise to a recent influx of papers [2-7] violations of causal locality everywhere, one would expect and books [8,9] on the subject. Several potentially use- the Hawking’s conjecture to be inapplicable in the frame- ful models for time machines have since been proposed, work of quantum gravity proper, and that the divergences including the wormhole of Thorne et al. -
Quantum Fluctuations and Thermodynamic Processes in The
Quantum fluctuations and thermodynamic processes in the presence of closed timelike curves by Tsunefumi Tanaka A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Montana State University © Copyright by Tsunefumi Tanaka (1997) Abstract: A closed timelike curve (CTC) is a closed loop in spacetime whose tangent vector is everywhere timelike. A spacetime which contains CTC’s will allow time travel. One of these spacetimes is Grant space. It can be constructed from Minkowski space by imposing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking’s chronology protection conjecture is correct, there must be a physical mechanism preventing the formation of CTC’s. Currently the most promising candidate for the chronology protection mechanism is the back reaction of the metric to quantum vacuum fluctuations. In this thesis the quantum fluctuations for a massive scalar field, a self-interacting field, and for a field at nonzero temperature are calculated in Grant space. The stress-energy tensor is found to remain finite everywhere in Grant space for the massive scalar field with sufficiently large field mass. Otherwise it diverges on chronology horizons like the stress-energy tensor for a massless scalar field. If CTC’s exist they will have profound effects on physical processes. Causality can be protected even in the presence of CTC’s if the self-consistency condition is imposed on all processes. Simple classical thermodynamic processes of a box filled with ideal gas in the presence of CTC’s are studied. If a system of boxes is closed, its state does not change as it travels through a region of spacetime with CTC’s. -
Redalyc.Quantization of Horizon Entropy and the Thermodynamics of Spacetime
Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Skákala, Jozef Quantization of Horizon Entropy and the Thermodynamics of Spacetime Brazilian Journal of Physics, vol. 44, núm. 2-3, -, 2014, pp. 291-304 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46431122018 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Braz J Phys (2014) 44:291–304 DOI 10.1007/s13538-014-0177-y PARTICLES AND FIELDS Quantization of Horizon Entropy and the Thermodynamics of Spacetime Jozef Skakala´ Received: 10 August 2013 / Published online: 20 February 2014 © Sociedade Brasileira de F´ısica 2014 Abstract This is a review of my work published in the basic results from some of the papers I published during papers of Skakala (JHEP 1201:144, 2012; JHEP 1206:094, that period [1–4]. It gives a more detailed discussion of the 2012) and Chirenti et al. (Phys. Rev. D 86:124008, 2012; results than the accounts in those papers, and it connects the Phys. Rev. D 87:044034, 2013). It offers a more detailed dis- results in [1–4] to certain conclusions recently reached by cussion of the results than the accounts in those papers, and other researchers. It also presents some new results, such it links my results to some conclusions recently reached by that provide additional support for the basic idea presented other authors.