Análise das características da evolução de campos de matéria em espaços-tempos simetricamente esféricos

Abstract

The main properties of the dynamics of matter fields in spherically symmetric spacetimes have been analyzed in this work,to do this, we take into account the metric for the different space-times, which will be encoded in the line element (space-time interval). Special attention was paid to the scalar field evolving around of black holes spacetimes. Some features of test field evolution, such as tortoise coordinate, effective potential, physical boundary conditions and oscillation modes were explored and discussed considering the asymptotic behavior of spacetimes being (AdS, Minkowski, dS). The normal and quasinormal frequencies of oscillation of the scalar field were calculated exactly for AdS, dS, Minkowski and BTZ black hole spacetimes, for which we use special functions that are solutions of known differential equations (Bessel, Hypergeometric). We also numerically calculate the quasinormal modes for the Schwarzschild and Schwarzschild-AdS spacetimes, using the spectral methods of series solutions (Frobenius and Bernstein).