  In this thesis, we present and apply the isomonodromy method (or
isomonodromic method) to the study of quasinormal modes (QNMs), more precisely,
we consider the analysis of modes that are associated with linear perturbations
in two distinct four-dimensional black holes one with angular momentum (Kerr)
and one with charge (Reissner-Nordstr\"om). We show, using the method, that the
quasinormal mode frequencies for both black holes can be analyzed with high
numerical accuracy and, for certain regimes, even analytically. We also
explore, by means of the equations involved, the regime in which both black
holes become extremal. We reveal for this case that through the isomonodromic
method, it is possible to calculate with good accuracy the values for the
quasinormal frequencies associated with gravitational, scalar, and
electromagnetic perturbations in the black hole with angular momentum, as well
as spinorial and scalar perturbations in the charged black hole. Extending thus
the analysis of the QNMs in the regime in which the methods used in the
literature have generally convergence problems.
