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Master's Dissertation
DOI
https://doi.org/10.11606/D.76.2020.tde-18052020-144531
Document
Author
Full name
Carolina Sayuri Takeda
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Hartmann, Betti (President)
Abramo, Luis Raul Weber
Saa, Alberto Vazquez
Title in English
Geodesic motion in the spacetime of two (un)equal mass black holes
Keywords in English
Black hole
Circular orbits
General relativity
Geodesic
Majumdar-Papapetrou metric
Abstract in English
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.
Title in Portuguese
Movimento geodésico no espaço-tempo de dois buracos negros de massas iguais e diferentes
Keywords in Portuguese
Buraco negro
Geodésica
Métrica de Majumdar-Papapetrou
Órbitas circulares
Relatividade geral
Abstract in Portuguese
Uma das principais abordagens usadas para estudar um certo espaço-tempo e entender sobre a sua estrutura, é a investigação de geodésicas. Este trabalho tem como objetivo explorar a métrica de Majumdar-Papetrou para um sistema binário de buracos negros, descrevendo buracos negros extremos de Reissner-Nordström. Este nome extremo é dado pelo fato de que o valor absoluto da carga é igual a massa dos buracos negros. Esta é uma situação de equilíbrio, pois a atração gravitacional é exatamente balanceada pela repulsão eletromagnética. Para uma análise mais completa, foram estudadas geodésicas tipo tempo e tipo luz para os casos de massas iguais e diferentes, também restringindo ao plano z = 0 e fora dele. Neste plano z = 0, a estabilidade das órbitas em relação ao raio ρ foi analisada e para a situação de massas iguais, foram estudadas órbitas limitadas e calculadas suas excentricidades. Através da inspeção de órbitas circulares e limitadas em diferentes cenários, foi possível encontrar regiões com órbitas circulares e estabelecer uma relação entre a quantidade dessas órbitas circulares e as massas dos buracos negros. Outra questão foi a análise do comportamento das órbitas quanto a diferenças extremas dos valores das massas. Todos esses estudos elucidaram a estrutura desse espaço-tempo binário de MP e podem se tornar o primeiro passo para compreender sistemas mais complexos, como múltiplos buracos negros.
 
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Publishing Date
2020-05-24
 
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