(Quasi-)normal modes of rotating black holes and solitons in Einstein-Gauss-Bonnet.
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Date
2025
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Universidad de Concepción
Abstract
Los parámetros que caracterizan cada espaciotiempo pueden influir directamente en el comportamiento de los modos cuasinormales. El análisis que se presentará comienza con el agujero negro de Bañados-Teitelboim-Zanelli (BTZ), una geometría en la que las frecuencias pueden calcularse analíticamente. A continuación, se aborda el agujero negro de Schwarzschild Anti-de Sitter (AdS), cuyo estudio requiere el uso de métodos numéricos. Finalmente, se investigan geometrías donde los modos no han sido explorados, específicamente soluciones a la teoría de Einstein-Gauss-Bonnet en el punto de Chern-Simons en cinco dimensiones.
En los resultados nuevos se consideran campos escalares sin masa para obtener las frecuencias sobre geometrías de solitones estáticos y agujeros negros rotantes. Estas se caracterizan por el momento angular j, la masa M y un parámetro de origen gravitacional b. El análisis se centra en el comportamiento de los modos como función del tamaño del solitón r0, junto con los parámetros j y b.
Comenzando por los solitones, se observa un comportamiento monótono de los modos normales a medida que b aumenta desde cero, mientras que ocurre una anomalía cuando r0 toma valores muy pequeños. Por otro lado, en el caso de los agujeros negros, se identifica una bifurcación en las frecuencias fundamentales al alcanzar un valor crítico del parámetro b. Además, al estudiar la variación de j, se distingue la existencia de dos ramas: una co-rotante y otra contra-rotante. Cada rama se identifica según su relación con el momento angular n del campo escalar.
The parameters that characterize each spacetime can directly influence the behavior of the quasi-normal modes. The analysis to be presented begins with the static BTZ black hole, a geometry in which frequencies can be calculated analytically. The Schwarzschild-AdS black hole is then discussed, whose study requires the use of numerical methods. Finally, geometries where the modes have not been explored are investigated, in particular solutions to the Einstein-Gauss-Bonnet theory at the Chern-Simons point in five dimensions. In the new results, massless scalar fields are considered to obtain the frequencies over static soliton and rotating black hole geometries. These are characterized by the angular momentum j, the mass M and a gravitational origin parameter b. The analysis focuses on the behavior of the modes as a function of the soliton size r0, along with the parameters j and b. Starting with solitons, a monotonic behavior of the normal modes is observed as b increases from zero, while an anomaly occurs when r0 takes small values. On the other hand, in the case of black holes, a bifurcation in the fundamental frequencies is identified when reaching a critical value of the parameter b. Furthermore, when studying the variation of j, the existence of two branches is distinguished: one co-rotating and the other counter-rotating. Each branch is identified according to its relation to the angular momentum n of the scalar field.
The parameters that characterize each spacetime can directly influence the behavior of the quasi-normal modes. The analysis to be presented begins with the static BTZ black hole, a geometry in which frequencies can be calculated analytically. The Schwarzschild-AdS black hole is then discussed, whose study requires the use of numerical methods. Finally, geometries where the modes have not been explored are investigated, in particular solutions to the Einstein-Gauss-Bonnet theory at the Chern-Simons point in five dimensions. In the new results, massless scalar fields are considered to obtain the frequencies over static soliton and rotating black hole geometries. These are characterized by the angular momentum j, the mass M and a gravitational origin parameter b. The analysis focuses on the behavior of the modes as a function of the soliton size r0, along with the parameters j and b. Starting with solitons, a monotonic behavior of the normal modes is observed as b increases from zero, while an anomaly occurs when r0 takes small values. On the other hand, in the case of black holes, a bifurcation in the fundamental frequencies is identified when reaching a critical value of the parameter b. Furthermore, when studying the variation of j, the existence of two branches is distinguished: one co-rotating and the other counter-rotating. Each branch is identified according to its relation to the angular momentum n of the scalar field.
Description
Tesis presentada para optar al grado de Magister en Ciencias con Mención en Física
Keywords
Relatividad generalizada (Física), Cosmología cuántica, Solitones