Thermodynamics of Asymptotically Locally AdS Spacetimes

By Ioannis Papadimitriou, Kostas Skenderis. 2005

461 citations recorded by the source corpus.

We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase space' techniques. This allows us to prove the first law of black hole mechanics for general asymptotically locally AdS black hole spacetimes. We illustrate our discussion by computing the conserved charges and verifying the first law for the four dimensional Kerr-Newman-AdS and the five dimensional Kerr-AdS black holes.

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

View Paper: https://www.semanticscholar.org/paper/bc0b58e6782196f70c7cdbb9fc79d0c59339f84e

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Citations in the corpus

Black hole chemistry: thermodynamics with Lambda (2016, methodology): “See also [46] for a treatment of the Smarr formula and first law with fixed Λ and the corresponding AdS/CFT interpretation.”
Holographic renormalization of general dilaton-axion gravity (2011, background): “Having completed this step, one not only has achieved a reformulation of the bulk dynamics in terms of a symplectic space of boundary data that can unambiguously be identified with the symplectic space of renormalized observables in any holographically dual theory, but also has automatically made th”
Lectures on Black Holes and the AdS3/CFT2 Correspondence (2006, background): “The stress tensors for higher dimensional spacetimes can be found in the literature [23,24], and additional related work appears in [25,21,26,27,28].”
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “ated as: q= m 1 + ag+ bg : (2.16) 4Regularity of the Euclidean section will be discussed further later. A general discussion of the thermodynamics of asymptotically locally AdS spaces can be found in [38]. { 7 { For later purposes we record the non-spacelike Killing vector arising as a bilinear of t”
The holographic universe (2010, background): “When the gravity approximation is valid throughout, the asymptotics yield sufficient information to uniquely reconstruct a regular bulk solution: the pair (g(0)ij , g(2σ)ij) (and similar for the scalar field) are coordinates in the covariant phase space of the gravitational theory [26].”
Real-time gauge/gravity duality: prescription, renormalization and examples (2008, background): “(As shown in [37], there is no diffeomorphism freedom at this order if we fix a boundary coordinate system and a boundary metric, so continuity of g(d)ab implies continuity of g(d)ij indeed.”
Topologically Massive Gravity and the AdS/CFT Correspondence (2009, background): “For theories that admit asymptotically (locally) AdS solutions finite conserved charges can always be obtained [22, 23, 24, 25, 26, 27] via the formalism of holographic renormalization [21].”
Kaluza-Klein Holography (2006, background): “Recall that in the 5d context all boundary terms, including counterterms, are uniquely fixed by the requirement that the variational problem is well posed with chosen boundary conditions [31].”
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, background): “A related question is to derive the above charges through holographic methods [32].”
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.”
Precision holography for non-conformal branes (2008, background): “One should note here that the local boundary counterterms are required, irrespectively of the issue of finiteness, by the more fundamental requirement of the well-posedness of the appropriate variational problem [41].”
AdS2 holographic dictionary (2016, methodology): “Instead, the fundamental property that determines the boundary counterterms is a well posed variational problem [70].”
Holographic gravitational anomalies (2005, background): “As explained in [12,26,1-6], the action and the stress tensor will diverge unless we include additional counterterms that are intrinsic to the boundary.”
Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT (2007, background): “Indeed, the divergences of the on-shell action are merely a manifestation of the fact that the variational problem is not formulated properly [31].”
Large rotating AdS black holes from fluid mechanics (2007, methodology): “The boundary stress tensor for the dual field theory on a unit sphere is given by [3–10] as”
Numerical methods for finding stationary gravitational solutions (2015, background): “[568] I.”