Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity

TL;DR

This paper proves that the Wald entropy of black holes in generalized quadric corrected Einstein-Maxwell gravity increases monotonically during quasistationary accretion, confirming the linearized second law of thermodynamics in this theory.

Contribution

It provides a generalized proof that the linearized second law holds for black holes in a broad class of modified gravity theories with electromagnetic coupling.

Findings

Wald entropy increases monotonically during accretion.

The second law holds under null energy condition and regular bifurcation surface assumptions.

The proof applies to linear order perturbations in the theory.

Abstract

Although the entropy of black holes in any diffeomorphism invariant theory of gravity can be expressed as the Wald entropy, the issue of whether the entropy always obeys the second law of black hole thermodynamics remains open. Since the nonminimal coupling interaction between gravity and the electromagnetic field in the general quadric corrected Einstein-Maxwell gravity can sufficiently influence the expression of the Wald entropy, we check whether the Wald entropy of black holes in the quadric corrected gravity still satisfies the second law. A quasistationary accreting process of black holes is first considered, which describes that black holes are perturbed by matter fields and eventually settle down to a stationary state. Two assumptions that the matter fields should obey the null energy condition and that a regular bifurcation surface exists on the background spacetime are further proposed. According to the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald entropy monotonically increases along the future event horizon under the linear order approximation of the perturbation. This result indicates that the Wald entropy of black holes in the quadric corrected gravity strictly obeys the linearized second law of thermodynamics.