Modified gravity R+F(G) and static spherically symmetric solutions

Considering an action in modified gravity, the static spherically symmetric solutions in vacuum are investigated. Introducing the Lagrangian multipliers α, we obtained the Lagrangian and equations of motion. For the constant Gauss-Bonnet invariant , the metric leads to de sitter solutions with and . Then for a large class of these models we obtain the exact solutions. Finally we study the thermodynamical quantities of these solutions. 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. The layout of the paper is the following. The action of gravity is considered and the field quations are derived, then the effect of modified gravity is considered as an effective stress-energy tensor. For the static spherically symmetric metric and using the method of Lagrangian multipliers to obtain the lagrangian and equations of motion is discussed. Then, the static spherically symmetric vacuum solutions for a large class of these metrics are investigated and the exact solutions are obtained.