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

## TL;DR

This paper explores static, spherically symmetric solutions in a modified gravity theory with quadratic curvature, analyzing their properties, singularities, horizons, and thermodynamics within the Einstein-Cartan formalism.

## Contribution

It presents exact and perturbative solutions in a quadratic curvature gravity model, including a de Sitter-like solution and a Schwarzschild-de Sitter perturbation, with analysis of their physical features.

## Key findings

- Found an exact de Sitter-like solution with vanishing torsion.
- Derived a perturbative Schwarzschild-de Sitter solution under specific conditions.
- Discussed classical singularities, horizons, and thermodynamic aspects of the solutions.

## 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.