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• W3098474166 abstract "It is well known that in general theories of gravity with the diffeomorphism symmetry, the black hole entropy is a Noether charge. But what will happen if the symmetry is explicitly broken? By investigating the covariant first law of black hole mechanics with background fields, we show that the Noether entropy is still applicable due to the local nature of the black hole entropy. Moreover, motivated by the proposal that the cosmological constant behaves as a thermodynamic variable, we allow the non-dynamical background fields to be varied. To illustrate this general formalism, we study a generic static black brane in the massive gravity. Using the first law and the scaling argument, we obtain two Smarr formulas. We show that both of them can be retrieved without relying on the first law, hence providing a self-consistent check of the theory." @default.
• W3098474166 created "2020-11-23" @default.
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• W3098474166 date "2017-06-01" @default.
• W3098474166 modified "2023-10-13" @default.
• W3098474166 title "First law of black hole mechanics in variable background fields" @default.
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• W3098474166 doi "https://doi.org/10.1007/s10714-017-2246-3" @default.
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