Leguéry, Monsieur Maxence (2023) Modes quasi-normaux en espaces-temps courbes PRE - Research Project, ENSTA.

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Abstract

The structure of the gravitational field is described by Einstein’s highly nonlinear equations of General Relativity. These equations, involving the metric of spacetime, possess a wide range of solutions, from black holes to homogeneous and isotropic Universes, for example. Once a specific spacetime is chosen, it is often beneficial to describe its behavior under small perturbations, known as quasinormal modes. These modes can be either scalar or tensorial in nature. The focus of this study is to investigate the scalar quasinormal modes of well-known spacetimes, such as Schwarzschild, Schwarzschild anti-de Sitter, and Kerr, to understand the methodology for applying it to the Taub-NUT spacetime, which represents the gravitational analogue of Dirac’s magnetic monopoles. We will primarily employ the Leaver method to numerically solve the scalar wave equation associated with a spacetime. After separating variables based on the symmetries of the considered spacetime, we will use the Frobenius method to expand the radial part of the wave equation into a power series, from which an equation whose quasinormal modes are the solutions can be derived. Through our analysis, we have highlighted essential characteristics of quasinormal modes in the Taub-NUT spacetime, shedding light on the underlying dynamics and enriching our understanding of this solution of Einstein’s equations. These research findings not only contribute to the vast field of general relativity but also pave the way for further investigations within the context of fluid/gravity holography, connecting gravitational dynamics in a spacetime to fluid-like dynamics on its boundary.

Item Type:Thesis (PRE - Research Project)
Uncontrolled Keywords:General relativity, quasinormal modes, Taub-NUT spacetime, numerical resolution, magnetic monopoles
Subjects:Physics, Optics
ID Code:9537
Deposited By:Maxence LEGUÉRY
Deposited On:24 août 2023 15:39
Dernière modification:24 août 2023 15:39

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