Banca de DEFESA: JOAO PAULO CAVALCANTE

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : JOAO PAULO CAVALCANTE
DATE: 30/06/2023
TIME: 10:00
LOCAL: Através de Videoconferência: https://meet.google.com/yqg-saaj-hbr
TITLE:

ISOMONODROMY METHOD AND BLACK HOLES QUASINORMAL MODES: numerical results and extremal limit analysis

KEY WORDS:

Linear perturbations. Quasinormal modes. Isomonodromic deformations.
Isomonodromic  functions.

PAGES: 148
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

Gravitational waves emitted by different astronomical sources, such as black
holes, are dominated by quasinormal modes (QNMs), damped oscillations at unique
frequencies that depend explicitly on the parameters that characterize the source of
gravitational waves. In the case of black holes, the parameters are charge, mass, angular
momentum, and overtones. These quasinormalmodes have been studied for a long time,
often to describe the time evolution of a given perturbation in a manner very similar to
what is done in the analysis of normal modes.

More recently, with the first detections of gravitational waves by the Laser
Interferometer Gravitational-Wave Observatory (LIGO), the study and analysis of
QNMs has become crucial, since they characterize the ringdown phase of a given
astronomical phenomenon, for example, the coalescence between two black holes or
between a black hole and a neutron star. In this phase, there is a superposition of QNMs
that, in turn, can be observed by the detectors and analyzed, allowing us to estimate the
values for the parameters associated with the astronomical source. Therefore, with the
advent of LIGO and other gravitational wave detectors, we have an excellent motivation
to study quasinormal modes.

From a theoretical point of view, there are in the literature a variety of methods
that through different theoretical approaches seek to calculate the quasinormal (QN)
frequencies. The best-known methods include; theWentzel-Kramers-Brillouin (WKB)
and Posch-Teller approximations, and the continued fraction method. In this thesis,
we present and apply the isomonodromy method (or isomonodromic method) to the
study of quasinormal modes, 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-Nordström).We show,
using the method, that the QN 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, we can 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 spinorial and scalar perturbations in the charged black hole.
Extending thus the analysis of QN frequencies in the regime in which the methods used
in the literature have generally convergence problems.

Through the separation of variables, we show that the equations describing
linear perturbations on both black holes can be rewritten in terms of second-order
ordinary differential equations (ODEs), where for the cases in which both black holes

are non-extremal and extremal, we have that such ODEs are the confluent and doubleconfluent
Heun equations, respectively. In turn, we consider the matrix representation
of the solutions of such ODEs and use the method of isomonodromic deformations,
which is based on the existence of families of linear matrix systems with the same
monodromy parameters that can be deformed isomonodromically. From the method,
we derive conditions for the isomonodromic functions + and  , which are strictly
connected with isomonodromic deformations in the confluent and double-confluent
Heun equations, respectively. By means of these conditions, we are able to perform
the numerical analysis of the QN frequencies for both black holes, in the extremal or
non-extremal regime.

Subsequently, making use of the representation of the two functions + and 
in terms of the Fredholm determinant, we show that it can be possible to reformulate,
through the isomonodromic method, the eigenvalue problem of the confluent and
double-confluent Heun equations into an initial value problem for both -functions. For
example, we reveal by means of the +-function that it is possible to obtain the values
of the QN frequencies for the non-extremal Kerr black hole. The same is observed for
the case in which the black hole is extremal, where one has that the frequencies are
obtained using the function  . For both regimes (non-extremal and extremal), it is
considered the analysis of the QN frequencies associated with linear perturbations of
gravitational, electromagnetic, and scalar fields in this black hole.

Finally, for the case of the charged Reissner-Nordström black hole, following
the same procedure applied to the Kerr black hole, we analyze the values of the QN
frequencies for the extremal and non-extremal Reissner-Nordström black hole. For both
cases, we present the results for the quasinormal frequencies associated with linear
perturbations of charged scalar and spinorial fields. In the analysis of theQNfrequencies
near extremality, we find that there is a critical value for the coupling between the charge
@ of the perturbing field and the charge & of the black hole, at which the quasinormal
frequencies become purely real when the black hole becomes extremal, i.e., frequencies
associated with normal modes.

COMMITTEE MEMBERS:
Externo à Instituição - MAURÍCIO RICHARTZ - UFABC
Externo à Instituição - OSCAR JOÃO CAMPOS DIAS
Presidente - 1508965 - BRUNO GERALDO CARNEIRO DA CUNHA
Interno - 2298925 - CLECIO CLEMENTE DE SOUZA SILVA
Interno - 1232688 - SHAHRAM JALALZADEH