Resumo:
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).
