Surface Terms of Quartic Quasitopological Gravity and Thermodynamics of Nonlinear Charged Rotating Black Branes

TL;DR

This paper introduces a well-defined surface term for quartic quasitopological gravity, finds charged black brane solutions, and studies their thermodynamics, including rotating cases, using the counterterm method and AdS/CFT inspired techniques.

Contribution

It provides the first well-defined variational principle for quartic quasitopological gravity and explores the thermodynamics of charged and rotating black branes within this framework.

Findings

Existence of black brane solutions with multiple horizons or naked singularities.

Thermodynamic quantities satisfy the first law of thermodynamics.

Charged rotating black branes are analyzed in higher dimensions.

Abstract

As in the case of Einstein or Lovelock gravity, the action of quartic quasitopological gravity has not a well-defined variational principle. In this paper, we first introduce a surface term that makes the variation of quartic quasitopological gravity well defined. Second, we present the static charged solutions of quartic quasitopological gravity in the presence of a non linear electromagnetic field. One of the branch of these solutions presents a black brane with one or two horizons or a naked singularity depending on the charge and mass of the solution. The thermodynamic of these black branes are investigated through the use of the Gibbs free energy. In order to do this, we calculate the finite action by use of the counterterm method inspired by AdS/CFT correspondence. Introducing a Smarr-type formula, we also show that the conserved and thermodynamics quantities of these solutions satisfy the first law of thermodynamics. Finally, we present the charged rotating black branes in $(n+1)$ dimensions with $k\leq [n/2]$ rotation parameters and investigate their thermodynamics.