Geodesic motion in the spacetime of two (un)equal mass black holes

• Autor(a) principal: Takeda, Carolina Sayuri
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/76/76131/tde-18052020-144531/
• topic: Black hole; Buraco negro; Circular orbits; General relativity; Geodesic; Geodésica; Majumdar-Papapetrou metric; Métrica de Majumdar-Papapetrou; Órbitas circulares; Relatividade geral

One of the main approaches to study a spacetime and understand its structure is through the investigation of geodesics. This work aims to explore the Majumdar-Papapetrou metric for a binary system of black holes, describing two extreme Reissner-Nordström black holes. The name extreme comes from the fact that the absolute value of the charge is equal to the mass of the black holes. This is a situation of equilibrium, since the gravitational attraction is exactly compensated by the electrical repulsion. For a more complete analysis, timelike and lightlike geodesics were studied for the cases of equal and different masses of the black holes, separating the cases in the plane z = 0 and away from it. In the plane z = 0, the stability of the orbits with respect to the radius ρ was analyzed and for the situation of equal masses, bounded orbits were studied and their eccentricities calculated. By examining circular and bounded orbits in different scenarios, it was possible to find parameter regions with circular orbits and establish a relation between the amount of possible circular orbits and the black holes masses. Another point was the evaluation of the behavior of orbits for extreme differences between the values of the masses. All of these studies brought some insights into the structure of this binary MP spacetime and might be a first step towards more complex systems, such as multi black holes.