On the positivity of energy in general relativity

Jang, Pong Soo

doi:10.1063/1.523776

Cited by 64 publications

(50 citation statements)

References 6 publications

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“…In particular, if is strictly stable as a MOTS, there exists an outward deformation strictly increasing θ + . InM = M × R, we consider Jang's equation [Jan78,SY81] for the graph of a func-…”

Section: Preliminariesmentioning

confidence: 99%

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Blowup of Jang’s Equation at Outermost Marginally Trapped Surfaces

Metzger

2009

Commun. Math. Phys.

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Abstract:The aim of this paper is to accurately describe the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence with an identifiable rate near a strictly stable MOTS.

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Section: Preliminariesmentioning

confidence: 99%

“…In this context, Jang's equation [SY81,Jan78] is an equation of prescribed mean curvature for the graph of a function in M × R. For details we refer to Sect. 2.…”

Section: Introductionmentioning

confidence: 99%

Blowup of Jang’s Equation at Outermost Marginally Trapped Surfaces

Metzger

2009

Commun. Math. Phys.

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“…The so-called Jang's equation [Jan78] is closely related to the equation θ + = 0. Both are prescribed mean curvature equations, where the right hand side depend on the normal.…”

Section: Introductionmentioning

confidence: 99%

The Area of Horizons and the Trapped Region

Andersson

Metzger

2009

Commun. Math. Phys.

115

325

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This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.

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“…They then observed [31] that theorem 1 (which is quite mysterious from a geometric point of view without the physical motivation) reduced to theorem 2 after solving a certain elliptic p.d.e. on (M 3 , g, h) called the Jang equation, named after the theoretical physicist who first introduced the equation in [19].…”

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confidence: 99%

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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On the positivity of energy in general relativity

Abstract: We show that the positive energy argument of Geroch for time-symmetric initial data sets can be generalized to general initial data sets.

Cited by 64 publications

References 6 publications

Blowup of Jang’s Equation at Outermost Marginally Trapped Surfaces

Blowup of Jang’s Equation at Outermost Marginally Trapped Surfaces

The Area of Horizons and the Trapped Region

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

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