On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions

TL;DR

This paper proposes a method to define energy for a broad class of static spherically symmetric black holes in higher order modified gravity, linking it to the integration constant and validating through thermodynamic principles.

Contribution

It introduces a novel energy expression for modified gravity black holes, derived from the equations of motion and thermodynamic laws, including new solutions with topological features.

Findings

Energy proportional to the solution's integration constant

Validation via the First Law of black hole thermodynamics

Discussion of a new topological higher derivative black hole

Abstract

In the case of a large class of static spherically symmetric black hole solutions in higher order modified gravity models, an expression for the associated energy is proposed and identified as a quantity proportional to the constant of integration, which appears in the explicit solution. The identification is achieved making use of derivation of the First Law of black hole physics from the equations of motion, evaluating independently the Entropy via Wald method and the Hawking temperature via the tunneling method. Several non trivial examples are discussed, including a new topological higher derivative black hole solution.