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- Title
Quasilocal Smarr relation for an asymptotically flat spacetime.
- Authors
Lee, Yein; Richards, Matthew; Stotyn, Sean; Park, Miok
- Abstract
We investigate the thermodynamics of Einstein–Maxwell (-dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a quasilocal Smarr relation from Euler's theorem. Then we calculate the quasilocal energy and surface pressure by employing a Brown–York quasilocal method along with Mann–Marolf counterterm and find entropy from the quasilocal thermodynamic potential. These quasilocal variables are consistent with the Tolman temperature and the entropy in a quasilocal frame turns out to be same as the Bekenstein–Hawking entropy. As a result, we found that a surface pressure term and its conjugate variable, a quasilocal area, do not participate in a quasilocal thermodynamic potential, but should be present in a quasilocal Smarr relation and the quasilocal first law of black hole thermodynamics. For dyonic black hole solutions having dynamic dilaton field, a non-trivial dilaton contribution should occur in the quasilocal first law but not in the quasilocal Smarr relation.
- Subjects
THERMODYNAMIC potentials; EULER theorem; SPACETIME; THERMODYNAMICS; BLACK holes
- Publication
European Physical Journal C -- Particles & Fields, 2021, Vol 81, Issue 4, p1
- ISSN
1434-6044
- Publication type
Article
- DOI
10.1140/epjc/s10052-021-09112-w