Sobre cálculo dos modos quasinormais e deflexão de luz devido a Wormholes e buracos negros

Abstract

Our goal in this work was to study some important properties about black holes and wormholes. Among the most important aspects we study we can divide them in two main topics. The first concerns the oscillation modes in systems such as black holes and wormholes. These systems must emit oscillations when they are disturbed by some external field. The amplitudes of these oscillations decrease with time. We typically call these oscillations quasi-normal modes QNMs. The second aspect we investigated, which has been attracting a lot of interest from researchers today, was gravitational lenses. Then we used the semi-analytical WKB method of third order and sixth order to compute the QNMs of some metrics addressed in this work. To compute the light deflection due to the influence of the gravitational lens, we use the Gauss-Bonnet theorem when we consider small deviations of the angles of the trajectories. The first two solutions we treat in this thesis were constructed based on the so-called bumblebee gravity, where the presence of Lorentz violation field contributes to the solution of Einstein equations. The first describes an exact black hole solution of the Schwarzschild type and the second a traversable wormhole, both dependent on a λ violation parameter. In the case of the wormhole solution in bumblebee gravity we determine which energy conditions are preserved to sustain this type of wormhole. We also determined the values that the parameter λ must assume, in order to allow us to calculate the QNMs using the WKB method. For the Schwarzschild solution in bumblebee gravity, it was also possible to determine the QNMs using the WKB method of third and sixth order. With the Gauss-Bonnet theorem we found an expression of the light deviation for small angles this time in Kalb-Ramond gravity. We further investigate two solutions of rotating black holes by calculating expressions of the deflection angle deviations using an extension of the Gauss-Bonnet theorem. The first solution describes a regular Kerr black hole and an Einstein-Bumblebee black hole in low rotation.