Narrow Results

In this paper, we study the geodesic structure for a geometry described by a spherically symmetric four-dimensional (4D) solution embedded in a five-dimensional (5D) space known as a brane-based spherically symmetric solution. Mainly, we have found that the extra dimension contributes to the existence of bounded orbits for the photons, such as planetary and circular stable orbits that have not been observed for other geometries.

From a variational action with nonminimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the non-minimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.

We study the Lifshitz black hole in four dimensions with dynamical exponent z = 2 and we calculate analytically the quasinormal modes of scalar perturbations. These quasinormal modes allow to study the stability of the Lifshitz black hole and we have obtained that Lifshitz black hole is stable.

We study the stability of z = 4 topological black hole in 4 + 1-dimensional Horava–Lifshitz gravity against scalar perturbations by analyzing the quasinormal modes (QNMs). It is possible to distinguish two cases for which the black hole is stable. The first one occurs when p + Q > 0 and QNMs are characterized by a real and imaginary part, meaning that the field has oscillatory modes but with Im(ω) < 0; therefore, it is stable. While in the second case p + Q < 0, QNMs are purely imaginary (Im(ω) < 0) and then absolutely damped.