Linearized second law of black hole thermodynamics for gravitational theory with higher-order interactions of matter fields

In the gravitational theory containing the second-order interaction of gravity with the scalar and electromagnetic fields at most, the black hole entropy obeying the linearized second law of black hole thermodynamics has been obtained. To generally study the linearized second law of black hole thermodynamics, we extend the gravitational theory to include higher-order interactions of gravity with the scalar and electromagnetic fields. We derive the general expression of black hole entropy satisfying the linearized second law, which is expressed as the Wald entropy with correction terms. It is worth noting that the correction terms consist of both the minimal and nonminimal coupling interactions between gravity and the scalar field, and the contribution of the electromagnetic field is not involved. Since the black hole entropy satisfying the linearized second law is determined only by the nonminimum coupling interactions in gravity according to the previous perspective, this result upends our understanding of the linearized second law in general gravitational theory.

Automated summary

In the gravitational theory with second-order interactions between gravity, scalar, and electromagnetic fields, a black hole entropy expression satisfying the linearized second law of black hole thermodynamics has been derived. By extending the gravitational theory to include higher-order interactions, the general expression of black hole entropy satisfying the linearized second law is obtained.