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Senovilla JMM. A critical appraisal of the singularity theorems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210174. [PMID: 35282689 DOI: 10.1098/rsta.2021.0174] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 09/13/2021] [Indexed: 06/14/2023]
Abstract
The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper, I briefly review the main ideas behind the theorems and then proceed to an evaluation of their hypotheses and implications. I will try to dispel some common misconceptions about the theorems and their conclusions, as well as to convey some of their rarely mentioned consequences. In particular, a discussion of space-time extensions in relation to the theorems is provided. The nature of the singularity inside black holes is also analysed. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.
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Affiliation(s)
- José M M Senovilla
- Department of Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
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Abstract
General relativity predicts its own demise at singularities but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were ultimately satisfied, spacetime singularities, although present, would not pose any practical problems to predictability. Here, we argue that under semiclassical effects, the situation should be rather different: the potential singularities which could appear in the theory will generically affect predictability, and so one will be forced to analyse whether there is a way to regularise them. For these possible regularisations, the presence and behaviour of matter during gravitational collapse and stabilisation into new structures will play a key role. First, we show that the static semiclassical counterparts to the Schwarzschild and Reissner–Nordström geometries have singularities which are no longer hidden behind horizons. Then, we argue that in dynamical scenarios of formation and evaporation of black holes, we are left with only three possible outcomes which could avoid singularities and eventual predictability issues. We briefly analyse the viability of each one of them within semiclassical gravity and discuss the expected characteristic timescales of their evolution.
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Bhattacharjee S, Kumar S, Sarkar S. Mass inflation and strong cosmic censorship in a nonextreme BTZ black hole. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.102.044030] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Zilberman N, Levi A, Ori A. Quantum Fluxes at the Inner Horizon of a Spherical Charged Black Hole. PHYSICAL REVIEW LETTERS 2020; 124:171302. [PMID: 32412272 DOI: 10.1103/physrevlett.124.171302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 03/09/2020] [Accepted: 04/03/2020] [Indexed: 06/11/2023]
Abstract
In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components ⟨T_{uu}⟩_{ren} and ⟨T_{vv}⟩_{ren} (u and v being the standard Eddington coordinates) of the renormalized stress-energy tensor for a minimally coupled massless quantum scalar field, in the vicinity of the inner horizon (IH) of a Reissner-Nordström black hole. These two flux components seem to dominate the effect of backreaction in the IH vicinity, and furthermore, their regularization procedure reveals remarkable simplicity. We consider the Hartle-Hawking and Unruh quantum states, the latter corresponding to an evaporating black hole. In both quantum states, we compute ⟨T_{uu}⟩_{ren} and ⟨T_{vv}⟩_{ren} in the IH vicinity for a wide range of Q/M values. We find that both ⟨T_{uu}⟩_{ren} and ⟨T_{vv}⟩_{ren} attain finite asymptotic values at the IH. Depending on Q/M, these asymptotic values are found to be either positive or negative (or vanishing in between). Note that having a nonvanishing ⟨T_{vv}⟩_{ren} at the IH implies the formation of a curvature singularity on its ingoing section, the Cauchy horizon. Motivated by these findings, we also take initial steps in the exploration of the backreaction effect of these semiclassical fluxes on the near-IH geometry.
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Affiliation(s)
- Noa Zilberman
- Department of Physics, Technion, Haifa 32000, Israel
| | - Adam Levi
- Department of Physics, Technion, Haifa 32000, Israel
| | - Amos Ori
- Department of Physics, Technion, Haifa 32000, Israel
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Chesler PM, Curiel E, Narayan R. Numerical evolution of shocks in the interior of Kerr black holes. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.99.084033] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Compère G. The Kerr/CFT correspondence and its extensions. LIVING REVIEWS IN RELATIVITY 2017; 20:1. [PMID: 28690421 PMCID: PMC5479153 DOI: 10.1007/s41114-017-0003-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/09/2016] [Accepted: 12/12/2016] [Indexed: 06/07/2023]
Abstract
We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy's formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy's formula. We follow an effective field theory approach and consider the Kerr-Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.
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Affiliation(s)
- Geoffrey Compère
- Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 231, 1050 Bruxelles, Belgium
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Garfinkle D. Numerical relativity beyond astrophysics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:016901. [PMID: 27819249 DOI: 10.1088/0034-4885/80/1/016901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Though the main applications of computer simulations in relativity are to astrophysical systems such as black holes and neutron stars, nonetheless there are important applications of numerical methods to the investigation of general relativity as a fundamental theory of the nature of space and time. This paper gives an overview of some of these applications. In particular we cover (i) investigations of the properties of spacetime singularities such as those that occur in the interior of black holes and in big bang cosmology. (ii) investigations of critical behavior at the threshold of black hole formation in gravitational collapse. (iii) investigations inspired by string theory, in particular analogs of black holes in more than 4 spacetime dimensions and gravitational collapse in spacetimes with a negative cosmological constant.
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Affiliation(s)
- David Garfinkle
- Department of Physics, Oakland University, Rochester, MI 48309, USA. Michigan Center for Theoretical Physics, Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA
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Interior Dynamics of Neutral and Charged Black Holes in f(R) Gravity. UNIVERSE 2015. [DOI: 10.3390/universe1020239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Marolf D, Ori A. Outgoing gravitational shock wave at the inner horizon: The late-time limit of black hole interiors. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.124026] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Compère G. The Kerr/CFT Correspondence and its Extensions. LIVING REVIEWS IN RELATIVITY 2012; 15:11. [PMID: 28179839 PMCID: PMC5255558 DOI: 10.12942/lrr-2012-11] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/13/2012] [Indexed: 05/30/2023]
Abstract
We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordström black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an SL(2, ℤ) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.
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Affiliation(s)
- Geoffrey Compère
- Physique Théorique et Mathématique, Université Libre de Bruxelles, CP 231, 1050 Bruxelles, Belgium
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Nakonieczna A, Rogatko M, Moderski R. Dynamical collapse of charged scalar field in phantom gravity. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.044043] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Maeda K, Okamura T, Koga JI. Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.85.066003] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Beauchesne H, Edery A. Emergence of a thin shell structure during collapse in isotropic coordinates. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.85.044056] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Winicour J. Characteristic Evolution and Matching. LIVING REVIEWS IN RELATIVITY 2012; 15:2. [PMID: 28163620 PMCID: PMC5253995 DOI: 10.12942/lrr-2012-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 01/04/2012] [Indexed: 05/27/2023]
Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black-hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black-hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.
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Affiliation(s)
- Jeffrey Winicour
- Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Potsdam-Golm, Germany
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 USA
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Borkowska A, Rogatko M, Moderski R. Collapse of charged scalar field in dilaton gravity. Int J Clin Exp Med 2011. [DOI: 10.1103/physrevd.83.084007] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Nakao KI, Harada T, Miyamoto U. Visible borders of spacetime generated by high-energy collisions. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.82.121501] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Doroshkevich A, Hansen J, Novikov D, Novikov I, Park DH, Shatskiy A. Physics of the interior of a black hole with an exotic scalar matter. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.81.124011] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Winicour J. Characteristic Evolution and Matching. LIVING REVIEWS IN RELATIVITY 2009; 12:3. [PMID: 28179825 PMCID: PMC5256078 DOI: 10.12942/lrr-2009-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/09/2009] [Indexed: 06/05/2023]
Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to eliminate the role of this artificial outer boundary via Cauchy-characteristic matching, by which the radiated waveform can be computed at null infinity. Progress in this direction is discussed.
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Affiliation(s)
- Jeffrey Winicour
- Albert Einstein Institute, Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, 14476 Potsdam-Golm, Germany
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 USA
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Winicour J. Characteristic Evolution and Matching. LIVING REVIEWS IN RELATIVITY 2005; 8:10. [PMID: 28179870 PMCID: PMC5256076 DOI: 10.12942/lrr-2005-10] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/19/2005] [Indexed: 05/27/2023]
Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed.
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Affiliation(s)
- Jeffrey Winicour
- Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm, Germany
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 USA
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Frolov AV, Kristjánsson KR, Thorlacius L. Semiclassical geometry of charged black holes. Int J Clin Exp Med 2005. [DOI: 10.1103/physrevd.72.021501] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Hansen J, Khokhlov A, Novikov I. Physics of the interior of a spherical, charged black hole with a scalar field. Int J Clin Exp Med 2005. [DOI: 10.1103/physrevd.71.064013] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Burko LM. Black-hole singularities: a new critical phenomenon. PHYSICAL REVIEW LETTERS 2003; 90:121101. [PMID: 12688862 DOI: 10.1103/physrevlett.90.121101] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2002] [Indexed: 05/24/2023]
Abstract
The singularity inside a spherical charged black hole, coupled to a spherical, massless scalar field is studied numerically. The profile of the characteristic scalar field was taken to be a power of advanced time with an exponent alpha>0. A critical exponent alpha(crit) exists. For exponents below the critical one (alpha<alpha(crit)) the singularity is a union of spacelike and null sectors, as is also the case for data with compact support. For exponents greater than the critical one (alpha>alpha(crit)) an all-encompassing, spacelike singularity evolves, which completely blocks the "tunnel" inside the black hole, preventing the use of the black hole as a portal for hyperspace travel.
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Affiliation(s)
- Lior M Burko
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
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Berger BK. Numerical Approaches to Spacetime Singularities. LIVING REVIEWS IN RELATIVITY 2002; 5:1. [PMID: 28179859 PMCID: PMC5256073 DOI: 10.12942/lrr-2002-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
This Living Review updates a previous version [25] which is itself an update of a review article [31]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
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Affiliation(s)
- Beverly K. Berger
- Physics Department, Oakland University, Rochester, MI 48309 USA
- Physics Division, National Science Foundation, 4201 Wilson Blvd., Arlington, VA 22230 USA
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Burko LM, Ori A. Analytic study of the null singularity inside spherical charged black holes. Int J Clin Exp Med 1998. [DOI: 10.1103/physrevd.57.r7084] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Berger BK. Numerical Approaches to Spacetime Singularities. LIVING REVIEWS IN RELATIVITY 1998; 1:7. [PMID: 28191836 PMCID: PMC5256114 DOI: 10.12942/lrr-1998-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
This review updates a previous review article [22]. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.
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Konkowski DA, Helliwell TM. Improved Cauchy horizon stability conjecture. Int J Clin Exp Med 1996; 54:7898-7901. [PMID: 10020799 DOI: 10.1103/physrevd.54.7898] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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