Static and spherically symmetric solutions in a scenario with quadratic curvature contribution

Abstract

In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein-Cartan formalism. The main goal consists in analyzing the behavior of the solutions under the influence of a quadratic curvature term in the presence of cosmological constant and no torsion. In the first incursion we found an exact de Sitter-like solution. This solution is obtained by imposing vanishing torsion in the field equations. On the other hand, by imposing vanishing torsion directly in the action, we are able to find a perturbative solution around the Schwarzschild-de Sitter usual solution. We briefly discuss classical singularities for each solution and the event horizons. A primer discussion on the thermodynamics of the geometrical solutions is also addressed.