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 behaviour 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 and cosmological horizons. A primer discussion on the thermodynamics of the geometrical solutions is also addressed.

Quadratic curvature terms and deformed Schwarzschild–de Sitter black hole analogues in the laboratory

“…The ratio ζ ≡ Λ 2 /(2 Λ2 ) regards a small parameter, since originally, Λ 2 Λ2 , at a minimum. Numerically manipulating the ratio ζ makes us to understand the influence of the quadratic curvature term in a perturbative way to solve the remaining differential equation [13]. The parameter ζ enforces Eq.…”

“…On the other hand, extensions and/or modifications of GR is in vogue since, for instance, the adventum of gauge theories of gravitation, to reach domains where GR are not well-succeeded. A novel induced gravity theory [12] was used to derive a perturbative solution around a Schwarzschild-de Sitter (SdS) geometry [13]. The core of such solution concentrates on understanding the influence of a quadratic curvature term in the field equations, even in a torsionless setup.…”

“…The arbitrariness investigated in Ref. [13] goes towards the implementation of perturbation methods to solve a differential equation extracted from every modified theory of gravity that sustains any contribution of a quadratic curvature. Furthermore, all kind of perturbative solutions in [13] can open doors towards investigations of the first simplified SdS black holes and their respective contributions to study their emission of gravitational waves from an astrophysical point of view.…”

“…[13] goes towards the implementation of perturbation methods to solve a differential equation extracted from every modified theory of gravity that sustains any contribution of a quadratic curvature. Furthermore, all kind of perturbative solutions in [13] can open doors towards investigations of the first simplified SdS black holes and their respective contributions to study their emission of gravitational waves from an astrophysical point of view. This study shall be here implemented through the duality between quasinormal modes emitted from such kind of black holes mergers and sound waves perturbations in a de Laval nozzle.…”

“…This section is devoted to briefly present the static, spherically symmetric solution, derived in Ref. [13], in-volving a quadratic curvature term.…”