The positive energy theorem for asymptotically anti-de Sitter spacetimes

Wang, Yaohua; Xie, Naqing; Zhang, Xiao

doi:10.1142/s0219199715500157

Cited by 15 publications

(29 citation statements)

References 28 publications

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“…Then Lemma 4.1 shows that Q is positive semi-definite. Same as [20], we can prove that the trace trQ, sum of the second-order minors Q (2) , sum of the third-order minors Q (3) and the determinant det Q are independent on t as well as on specific Clifford representation. Their nonnegativity gives rise to (1.1).…”

Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 76%

“…and λ 1 , λ 2 , λ 3 , λ 4 are four arbitrary complex numbers [20]. The Killing spinor Φ 0 along M is given by fixing t in Φ λ 0 .…”

Section: Dirac Equationmentioning

confidence: 99%

“…Let U αβ be the restrictions of the Killing vectors on the t-slice (cf. Appendix A [20]). Given ε > 0, ρ > 0, we introduce the following ten pre total energymomentum…”

Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 99%

“…As in [20], we denote c = (c 1 , c 2 , c 3 ), c ′ = (c ′ 1 , c ′ 2 , c ′ 3 ), J = (J 1 , J 2 , J 3 ) and…”

Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 99%

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Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

Wang

Zhang

2019

Int. J. Math.

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We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition. Dedicate to Professor Luen-Fai Tam on the occasion of his 70th birthdayThe following lemma can be proved using Lemma 3.2 Lemma 3.3. Let ∇ * , D * be the adjoint operators of ∇, D respectively. If the weak dominant energy condition holds, then, for any φ ∈ H 1 (S),

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Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 76%

“…and λ 1 , λ 2 , λ 3 , λ 4 are four arbitrary complex numbers [20]. The Killing spinor Φ 0 along M is given by fixing t in Φ λ 0 .…”

Section: Dirac Equationmentioning

confidence: 99%

“…Let U αβ be the restrictions of the Killing vectors on the t-slice (cf. Appendix A [20]). Given ε > 0, ρ > 0, we introduce the following ten pre total energymomentum…”

Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 99%

“…As in [20], we denote c = (c 1 , c 2 , c 3 ), c ′ = (c ′ 1 , c ′ 2 , c ′ 3 ), J = (J 1 , J 2 , J 3 ) and…”

Section: Total Energy-momentum and Proof Of Theorem 12mentioning

confidence: 99%

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Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

Wang

Zhang

2019

Int. J. Math.

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“…Initial investigations were carried out in [1,3,27,30], the time symmetric case (k = 0) was treated in [2,18,19,49,53], and the most general versions were given in [20,38,50,52]. See also [15] for a discussion concerning the rigidity statement.…”

Section: The Positive Mass Theoremmentioning

confidence: 99%

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

Sle

Khuri

2017

Gen Relativ Gravit

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Abstract. We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbolic setting from counterparts in the asymptotically flat realm, whenever a geometrically motivated system of elliptic equations admits a solution. The inequalities treated here relate mass, angular momentum, charge, and horizon area.

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The Rest Mass of an Asymptotically Anti-de Sitter Spacetime

Chen

Hung

Wang

et al. 2017

Ann. Henri Poincaré

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Abstract. We study the space of Killing fields on the four dimensional AdS spacetime AdS 3,1 . Two subsets S and O are identified: S (the spinor Killing fields) is constructed from imaginary Killing spinors, and O (the observer Killing fields) consists of all hypersurface orthogonal, future timelike unit Killing fields. When the cosmology constant vanishes, or in the Minkowski spacetime case, these two subsets have the same convex hull in the space of Killing fields. In presence of the cosmology constant, the convex hull of O is properly contained in that of S. This leads to two different notions of energy for an asymptotically AdS spacetime, the spinor energy and the observer energy. In [10], Chruściel, Maerten and Tod proved the positivity of the spinor energy and derived important consequences among the related conserved quantities. We show that the positivity of the observer energy follows from the positivity of the spinor energy. A new notion called the "rest mass" of an asymptotically AdS spacetime is then defined by minimizing the observer energy, and is shown to be evaluated in terms of the adjoint representation of the Lie algebra of Killing fields. It is proved that the rest mass has the desirable rigidity property that characterizes the AdS spacetime.

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The positive energy theorem for asymptotically anti-de Sitter spacetimes

Cited by 15 publications

References 28 publications

Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

Transformations of asymptotically AdS hyperbolic initial data and associated geometric inequalities

The Rest Mass of an Asymptotically Anti-de Sitter Spacetime

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