Deflexão gravitacional de partículas e o teorema de Gauss-Bonnet

Abstract

In this work, we investigate the gravitational bending angle due to the spacetimes of two matters. The first is the bumblebee model, and the second is the Casimir wormholes. The bumblebee black holes break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. Casimir wormholes consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP) corrections of Casimir energy. We use the Ishihara method for the Jacobi metric, which allows us to study the bending angle of light and massive test particles for finite distances. In the bumblebee model, we consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant. For the Casimir wormholes, beyond the uncorrected Casimir source, we consider many GUP corrections, namely: the Kempf, Mangano and Mann (KMM) model, the Detournay, Gabriel and Spindel (DGS) model, and the so-called type II model for the GUP principle. We also find the deflection angle of light and massive particles in the case the receiver and the source are far away from the lens for each spacetime considered.