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Title: Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N = 2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries andmore » those of the BTZ black hole. Finally, surface terms play a crucial role in this identification.« less
Authors:
 [1] ;  [2] ;  [3]
  1. International School for Advanced Studies (SISSA), Trieste (Italy); National Inst. of Nuclear Physics (INFN), Trieste (Italy); Kim Il Sung Univ., Pyongyang (Korea, Democratic People's Republic of). Dept. of Physics; International Centre for Theoretical Physics (ICTP), Trieste (Italy)
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics
  3. International School for Advanced Studies (SISSA), Trieste (Italy); National Inst. of Nuclear Physics (INFN), Trieste (Italy)
Publication Date:
OSTI Identifier:
1326991
Grant/Contract Number:
SC0013528
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Univ. of Pennsylvania, Philadelphia, PA (United States); International School for Advanced Studies (SISSA), Trieste (Italy); National Inst. of Nuclear Physics (INFN), Trieste (Italy)
Sponsoring Org:
USDOE; International Inst. of Physics (IIP) (Brazil); Slovenian Research Agency (ARRS) (Slovenia)
Contributing Orgs:
International Centre for Theoretical Physics (ICTP), Trieste (Italy); Univ. of Maribor (Slovenia)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; black holes; black holes in string theory; gauge-gravity correspondence