We study the gravitational vacuum star (gravastar) configuration as proposed by [1] in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime.

Recently, a fully covariant version of the theory of F (T ) torsion gravity has been introduced [1]. In covariant F (T ) gravity the Schwarzschild solution is not a vacuum solution for F (T ) = T and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with F (T ) = T + (α/2) T 2 , representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, α, which governs deviations from General Relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the solar system or greater universe could be attributable to nonlinear torsion.

Using the improved quantization technique to the minisuperspace approximation of loop quantum gravity, we study the evolution of black holes supported by a cosmological constant. The addition of a cosmological constant allows for classical solutions with planar, cylindrical, toroidal, and higher-genus black holes. Here we study the quantum analog of these space-times. In all scenarios studied, the singularity present in the classical counterpart is avoided in the quantized version and is replaced by a bounce, and in the late evolution, a series of less severe bounces. Interestingly, although there are differences during the evolution between the various symmetries and topologies, the evolution on the other side of the bounce asymptotes to space-times of Nariai-type, with the exception of the planar black hole analyzed here, whose T-R ¼ constant subspaces seem to continue expanding in the long-term evolution. For the other cases, Nariai-type universes are attractors in the quantum evolution, albeit with different parameters. We study here the quantum evolution of each symmetry in detail.