Static Spherically Symmetric Solutions in General Gauss-Bonnet Gravity

TL;DR

This paper explores static spherically symmetric solutions in F(G) modified gravity, deriving new metrics and analyzing black hole thermodynamics within this theoretical framework.

Contribution

It introduces a method to find solutions in F(G) gravity, including a new metric, and investigates their thermodynamic properties.

Findings

Derived Schwarzschild-de Sitter and new metric solutions.

Analyzed event horizon, Hawking temperature, and thermodynamics.

Provided insights into black hole behavior in Gauss-Bonnet modified gravity.

Abstract

Considering an action in F(G) modified gravity, the static spherically symmetric solutions are investigated. Introducing the Lagrangian multipliers {\alpha} we obtain the Lagrangian and equations of motion. we obtain two type solutions for these models. The first case leads to Schwarzschild-de Sitter (anti de Sitter) solution and the other one, results in a new metric. At last, the event horizon, the Hawking temperature and the generalized second law of thermodynamics in the framework of the modified Gauss-Bonnet gravity for this solution as a black hole are investigated.