Classical perturbations of AdS spacetimes.
Loading...
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de Concepción
Abstract
En esta tesis estudiaremos las perturbaciones gravitacionales de espaciotiempos asintóticamente anti-de Sitter (AdS) en cuatro dimensiones, usando la maquinaria desarrollada por Chandrasekhar, la cual se basa en el uso de una métrica general, axisimétrica y que puede depender del tiempo, escrita en el formalismo de tétradas. Este formalismo desacopla naturalmente las perturbaciones de los modos axiales (impares) y los modos polares (pares), y permite expresas sus ecuaciones como ecuaciones tipo Shroedinger.
Usaremos este método en dos backgrounds distintos: Schwarzschild AdS y el solitón AdS. En el primer caso obtenemos potenciales efectivos para ambos modos, axial y polar, y verificamos que coinciden con los potenciales encontrados en la literatura, también enfatizamos que la isoespectralidad se rompe cuando el espaciotiempo es asintóticamente AdS. En el segundo caso hacemos un análisis similar, logrando obtener una ecuación para las perturbaciones axiales la cual pudimos resolver numericaménte para determinar los modos normales del solitón AdS, mostrando que coinciden con los resultados encontrados en la literatura.
concluimos que el método de Chandrasekhar que fue originalmente planteado para espaciotiempos asintóticamente planos puede ser extendido exitosamente a espaciotiempos con constante cosmológica negativa, incluyendo espaciotiempos que son regulares en todas partes, como el solitón AdS.
In this thesis we study the gravitational perturbations in four dimensional asymptotically anti-de Sitter (AdS) backgrounds using the approach developed by Chandrasekhar, which is based in a general time-dependent axisymmetric metric worked in the tetrad frame. This formalism allows to naturally decouple the perturbation of axial (odd) modes and polar (even) modes, and to express their equations as second order Schroedinger-like ones. We apply the method to two different backgrounds: Schwarzschild-AdS and the AdS soliton. In the first case, we obtain effective potentials for both modes, axial and polar, and we verify that they correspond to the potentials found in literature by other methods and we emphasise how the isospectrality is broken by the presence of a negative cosmological constant. In the second case we perform a similar analysis, obtaining the differential equation for the axial perturbation. We were able to solve it numerically to obtain the normal modes of the AdS soliton, showing that they are in agreement with the results obtained by Constable and Myers in. We conclude that Chandrasekhar’s approach originally formulated for asymptotically flat spacetimes, can be successfully extended to spacetimes with a negative cosmological constant, including spacetimes which are regular everywhere, such as the AdS soliton.
In this thesis we study the gravitational perturbations in four dimensional asymptotically anti-de Sitter (AdS) backgrounds using the approach developed by Chandrasekhar, which is based in a general time-dependent axisymmetric metric worked in the tetrad frame. This formalism allows to naturally decouple the perturbation of axial (odd) modes and polar (even) modes, and to express their equations as second order Schroedinger-like ones. We apply the method to two different backgrounds: Schwarzschild-AdS and the AdS soliton. In the first case, we obtain effective potentials for both modes, axial and polar, and we verify that they correspond to the potentials found in literature by other methods and we emphasise how the isospectrality is broken by the presence of a negative cosmological constant. In the second case we perform a similar analysis, obtaining the differential equation for the axial perturbation. We were able to solve it numerically to obtain the normal modes of the AdS soliton, showing that they are in agreement with the results obtained by Constable and Myers in. We conclude that Chandrasekhar’s approach originally formulated for asymptotically flat spacetimes, can be successfully extended to spacetimes with a negative cosmological constant, including spacetimes which are regular everywhere, such as the AdS soliton.
Description
Tesis presentada para optar al grado de Magíster en Física
Keywords
Black holes (Astronomy), Solitons, Perturbation (Astronomy)