Static Spherically Symmetric Solutions in General Gauss-Bonnet Gravity

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.