Estudo de soluções esfericamente simétricas em teorias estendidas da gravitação

Abstract

The k-essence theory is characterized by a function of the kinetic term of a scalar field. This theory was widely applied in cosmology, suggested as dark energy and in an attempt to explain the inflationary period. Rastall’s gravity originates from the non-zero divergence of the energy-moment tensor, that is, it is a non-conservative theory. Another important feature of this theory is that it does not originate from the variational principle. However, in cosmology, Rastall’s theory leads to results similar to the #CMD, differing only in the nonlinear regime of the evolution of cosmic perturbations. In the context of compact objects, the results obtained in neutron stars are quite interesting using Rastall’s theory. The big surprise is that, even though theories are so different, their solutions in static and spherically symmetrical spacetime are the same, in some cases. Due to this fact, a study to investigate in which situations these two theories can be dual. However, the study of the stability of the solutions in k-essence and Rastall show us that these two theories do not coincide at the perturbation level. The attempt to find new dilatonic solutions in a static and spherically symmetric geometry revealed a set of new solutions for black holes, wormholes and even singularities. Rotating black holes are astrophysical objects found in nature, so the study of these objects is of great importance. However, finding new rotating black hole solutions can be quite a difficult task. A rotating black hole is described by a stationary metric and this fact makes it more difficult to solve Einstein’s equations. In this sense, the use of mathematical methods that convert known static solutions into stationary solutions is welcome. We will discuss the viability of this process.