Conserved charges in various theories of gravity

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2022-9
Özşahin, Hikmet
The first law of black hole thermodynamics in the presence of a cosmological constant $\Lambda$ can be generalized by introducing a term containing the variation $\delta\Lambda$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc and it has been shown in \cite{1} that the new term has the same structure: $\Lambda$ is a conserved charge associated with a gauge symmetry. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the ``effective volume" of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of ``$\Lambda$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Specially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well-defined in principle

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Citation Formats
H. Özşahin, “Conserved charges in various theories of gravity,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.