Hikmet Özşahin | Searcharxiv

arXiv2026

Microscopic entropy of regular BTZ black holes in 3d Lovelock gravity at all orders

We give a microscopic derivation of the semi-classical entropy of the black holes of 3d Lovelock gravity with an infinite tower of regularized Lovelock corrections, which include the regular BTZ black holes found recently. Working in the mini-superspace formalism, we show that the reduced action and its boundary term can be obtained in closed form at all orders in terms of the generating function of the couplings. Assuming the ground state is described by the soliton obtained from the static black hole by a double Wick rotation, we compute the soliton mass and reproduce the semi-classical entropy from the Cardy formula without central charges for arbitrary couplings. We then extend the mini-superspace to stationary configurations, compute the mass and the angular momentum of the rotating black holes obtained by a boost, and verify the Cardy formula in the presence of rotation.

hep-th↗

arXiv2021

First law of black hole thermodynamics and Smarr formula with a cosmological constant

The first law of black hole thermodynamics in the presence of a cosmological constant $Λ$ can be generalized by introducing a term containing the variation $δΛ$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc., it has been shown [Classical Quantum Gravity 35, 125012 (2018)] that the new term has the same structure: $Λ$ is a conserved charge associated with a gauge symmetry; and its role in the first law is quite similar to an ``electric charge" rather than to the pressure. Besides, its conjugate chemical potential resembles an ``electric potential" on the horizon, in contrast with the volume enclosed by horizon. 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 ``$Λ$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Especially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well defined in principle.

gr-qc↗