Perturbative analysis of black holes via the isomonodromic method

• Grant number: 24/15921-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2025
• End date: January 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Maurício Richartz
• Grantee: João Paulo Cavalcante
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

In this project, we will explore advanced aspects of black hole physics and their perturbations using the isomonodromic method. Our initial focus will be to investigate superradiant instability and the behavior of frequencies for massive scalar perturbations in the Kerr-Newman black hole as it approaches extremality, employing the Riemann-Hilbert map for the confluent Heun equation and associated conditions for quasi-normal modes and quasi-bound states. We will also examine, through this method, scalar clouds around Kerr and Kerr-Newman black holes, which are stationary solutions to the Klein-Gordon equation describing scalar fields around the black hole. Additionally, we will address exceptional points and hysteresis phenomena for perturbations in the Kerr-Newman black hole, investigating the relationship between these points and geometric phases. To this end, we will examine how infinitesimal variations in the parameters of interest are related to the crossings between quasi-normal mode frequencies and the occurrence of hysteresis. Finally, we will apply the isomonodromic method to the study of analogue models of gravity and modified theories of gravitation, analyzing quasi-normal modes and investigating the presence of phenomena such as hysteresis and exceptional points in these models.