The positive energy conjecture and the cosmic censor hypothesis

Jang, Pong Soo; Wald, Robert M.

doi:10.1063/1.523134

Cited by 122 publications

(106 citation statements)

References 11 publications

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“…As introduced by Geroch [13] and Jang-Wald [20], a smooth family of surfaces Σ(t) in (M 3 ,ḡ) is said to satisfy inverse mean curvature flow if the speed in the outward normal direction of the family of surfaces as t increases at each point is equal to 1/H, whereH > 0 is the mean curvature of the surface at that point. This flow has the important and surprising property that the Hawking mass of Σ(t) is nondecreasing when (M 3 ,ḡ) has nonnegative scalar curvatureR.…”

Section: Conjecture 9 Equation 62 Implies the Hypotheses Of Lemmamentioning

confidence: 99%

“…However, in [29] Penrose argued using the cosmic censor conjecture that future apparent horizons, which are defined in terms of local geometry, must be enclosed by event horizons. Thus, the area ofΣ serves as a lower bound for the total area of the event horizons [20], [17], and the Penrose conjecture follows. This same argument, but run in the opposite time direction, yields the same conjecture for past apparent horizons as well.…”

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confidence: 99%

“…If Σ 2 ∈ S is a zero mean curvature surface, then is already a connected component of the outermost minimal area surface of (M 3 , g) by Meeks-Simon-Yau [26].) Their method of proof, first proposed by the theoretical physicists Geroch [13] and Jang-Wald [20], uses a parabolic technique called inverse mean curvature flow. Starting with a connected zero mean curvature surface, HuiskenIlmanen found a weak definition of inverse mean curvature flow, where the surface is flowed out at each point in (M 3 , g) with speed equal to the reciprocal of the mean curvature of the surface at that point, for almost every surface in the flow.…”

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confidence: 99%

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P. D. E.'s Which Imply the Penrose Conjecture

Bray¹,

Khuri²

2011

Asian Journal of Mathematics

130

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Abstract. In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool in our method is the derivation of a new identity which we call the generalized Schoen-Yau identity, which is of independent interest. Using a generalized Jang equation, we use this identity to propose canonical embeddings of Cauchy data into corresponding static spacetimes. In addition, we discuss the Carrasco-Mars counterexample to the Penrose conjecture for generalized apparent horizons (added since the first version of this paper was posted on the arXiv) and instead conjecture the Penrose inequality for time-independent apparent horizons, which we define.

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Section: Conjecture 9 Equation 62 Implies the Hypotheses Of Lemmamentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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P. D. E.'s Which Imply the Penrose Conjecture

Bray¹,

Khuri²

2011

Asian Journal of Mathematics

130

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“…(This inequality is similar to, though distinct from, the Gibbons-Penrose isoperimetric inequality for initial data sets in general relativity which has its inspiration from this inequality [20][21][22][23][24].) That such an inequality should hold can be argued as follows.…”

Section: Introductionmentioning

confidence: 99%

Just how long can you live in a black hole and what can be done about it?

Burnett

1995

Phys. Rev. D

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We study the problem of how long a journey within a black hole can last. Based on our observations, we make two conjectures. First, for observers that have entered a black hole from an asymptotic region, we conjecture that the length of their journey within is bounded by a multiple of the future asymptotic "size" of the black hole, provided the spacetime is globally hyperbolic and satisfies the dominant-energy and non-negative-pressures conditions. Second, for spacetimes with R 3 Cauchy surfaces (or an appropriate generalization thereof) and satisfying the dominant energy and non-negative-pressures conditions, we conjecture that the length of a journey anywhere within a black hole is again bounded, although here the bound requires a knowledge of the initial data for the gravitational field on a Cauchy surface. We prove these conjectures in the spherically symmetric case. We also prove that there is an upper bound on the lifetimes of observers lying "deep within" a black hole, provided the spacetime satisfies the timelike-convergence condition and possesses a maximal Cauchy surface. Further, we investigate whether one can increase the lifetime of an observer that has entered a black hole, e.g., by throwing additional matter into the hole. Lastly, in an appendix, we prove that the surface area A of the event horizon of a black hole in a spherically symmetric spacetime with ADM mass MADM is always bounded by A ≤ 16πM 2 ADM , provided that future null infinity is complete and the spacetime is globally hyperbolic and satisfies the dominant-energy condition.

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“…which is called the Cosmic Censorship Inequality (CCI) or Cosmic Censorship Bound (CCB) [16] and which is a necessary condition for Cosmic-Censorship hypothesis (CCH) [15] (See [17][18][19][20][21]). We derive this inequality for these class of BHs.…”

Section: Introductionmentioning

confidence: 99%

Area Products for H± in AdS Space

Pradhan¹

2017

Galaxies

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Abstract:We derive the thermodynamic products, in particular the area (or entropy) products of H ± for a wide variety of black holes (BHs) in anti-de Sitter (AdS) space. We show by explicit and exact calculations that, for this class of BHs, more complicated functions of the event horizon area and Cauchy horizon area are indeed mass-independent. This mass-independent results indicate that they could turn out to be a "universal" quantity provided that they depend only on the quantized angular momentum, quantized charges, and cosmological constant, etc. Furthermore, these area (or entropy) product relations for several classes of BHs in AdS space gives us strong indication to understanding the nature of non-extremal BH entropy (both inner and outer) at the microscopic level. Moreover, we compute the famous Cosmic Censorship Inequality (which requires Cosmic-Censorship hypothesis) for these classes of BHs in AdS space. Local thermodynamic stability has been discussed for these BHs and under certain conditions, these classes of BHs displayed second order phase transition. The super-entropic BH does not provide any kind of second order phase transition.

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The positive energy conjecture and the cosmic censor hypothesis

Abstract: We show that a positive energy argument of Geroch can be modified to rule out a possible class of counterexamples to the cosmic censor hypothesis proposed by Penrose.

Cited by 122 publications

References 11 publications

P. D. E.'s Which Imply the Penrose Conjecture

P. D. E.'s Which Imply the Penrose Conjecture

Just how long can you live in a black hole and what can be done about it?

Area Products for H± in AdS Space

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