Publications

THESIS - Isomonodromy Method and Black Holes Quasinormal Modes: numerical results and extremal limit analysis

Published in Arxiv, 2023

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-Nordström). 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.

Expansions for semiclassical conformal blocks

Published in To be published, 2022

We propose a relation the expansions of regular and irregular semiclassical conformal blocks at different branch points making use of the connection between the accessory parameters of the BPZ decoupling equations to the logarithm derivative of isomonodromic tau functions. We give support for these relations by considering two eigenvalue problems for the confluent Heun equations obtained from the linearized perturbation theory of black holes. We first derive the large frequency expansion of the spheroidal equations, and then compare numerically the excited quasi-normal mode spectrum for the Schwarzschild case obtained from the large frequency expansion to the one obtained from the low frequency expansion and with the literature, indicating that the relations hold generically in the complex modulus plane.

Scalar and Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents

Published in Phys. Rev. D 104, 124040, 2021

We investigate spin-0 and spin-1/2 perturbations for nonextremal and extremal Reissner-Nordström backgrounds using the isomonodromic method. We calculate the fundamental quasinormal modes (QNMs) associated with each perturbation as a function of the electromagnetic coupling qQ and ratio Q/M. After corroborating the literature values for generic qQ and Q/M, we turn to study the near-extremal limit. In parallel with the study of QNMs for the Kerr geometry, we find the existence of “nondamping” modes for qQ above a spin-dependent critical value and locate the bifurcation point in the q−Q parameter space.

Teukolsky master equation and Painlevé transcendents: Numerics and extremal limit

Published in Phys.Rev.D 104 8, 084051, 2021

We conduct an analysis of the quasinormal modes for generic spin perturbations of the Kerr black hole using the isomonodromic method. The strategy consists of solving the Riemann-Hilbert map relating the accessory parameters of the differential equations involved to monodromy properties of the solutions, using the τ-function for the Painlevé V transcendent. We show excellent accordance of the method with the literature for generic rotation parameter a<M. In the extremal limit, we determined the dependence of the modes with the black hole temperature and establish that the extremal values of the modes are obtainable from the Painlevé V and III transcendents.

Confluent conformal blocks and the Teukolsky master equation

Published in Phys.Rev.D 102 10, 105013, 2020

Quasinormal modes of usual, four-dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert problem, which was recently solved in terms of the Painlevé V transcendent. We use this formulation to generate small-frequency expansions for the angular spheroidal harmonic eigenvalue and derive conditions on the monodromy properties for the radial modes. Using exponentiation, we relate the accessory parameter to a semiclassical conformal description and discuss the properties of the operators involved. For the radial equation, while the operators at the horizons have Liouville momenta proportional to the entropy intake, we find that spatial infinity is described by a Whittaker operator.

João Cavalcante