Comparison between various notions of conserved charges in asymptotically AdS spacetimes

By S. Hollands, A. Ishibashi, D. Marolf. 2005

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We derive Hamiltonian generators of asymptotic symmetries for general relativity with asymptotic AdS boundary conditions using the ‘covariant phase space’ method of Wald et al. We then compare our results with other definitions that have been proposed in the literature. We find that our definition agrees with that proposed by Ashtekar et al, with the spinor definition, and with the background-dependent definition of Henneaux and Teitelboim. Our definition disagrees with that obtained from the ‘counterterm subtraction method’, but the difference is found to consist only of a ‘constant offset’ that is determined entirely in terms of the boundary metric. We finally discuss and justify our boundary conditions by a linear perturbation analysis, and we comment on generalizations of our boundary conditions, as well as inclusion of matter fields.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b2661e5edca763c292da3693679a585c0566e03d

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Citations in the corpus

Holographic gravitational anomalies (2005, background): “The AdS/CFT correspondence asserts that T ij is the expectation value of the stress tensor in a CFT defined on a space with metric conformal to g (0) ij . This relation has been the subject of much work, e.g. [ 1-6 ].”
Thermodynamics of black holes in two (and higher) dimensions (2007, result): “This is the same result obtained in higher dimensions using any one of a number of methods [55].”
Gravitation from entanglement in holographic CFTs (2013, background): “This is confirmed for Einstein gravity in [31, 32], and rather generally in [33], but these discussions rely on the equations of motion.”
Surface charge algebra in gauge theories and thermodynamic integrability (2007, background): “Recent related work can be found for instance in [24, 25, 26, 27, 28, 29, 30, 31, 32, 33].”
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, background): “(4.14) Hence, since ηr and ξm are independent, the asymptotic AdS symmetry fixes the functional relationship between a and b to be of the form (4.3) given above.”
Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes (2005, background): “For a diffeomorphism ξ that is an isometry, the total variation ¯ δ vanishes and then all the functional variations of the fields in � are replaced by the corresponding Lie derivative δϕ = −L�ϕ (see also [22] and, for a recent discussion, [ 23 , 24]).”