Analysis of Quasinormal modes of Schwarzschild and de Sitter black hole in horizon-penetrating coordinates

Gaur, Shashwat (2025) Analysis of Quasinormal modes of Schwarzschild and de Sitter black hole in horizon-penetrating coordinates. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Shashwat Gaur (20MS197)) 20MS197_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (773kB)

Abstract

Quasi-normal Modes can be thought of as the characteristics modes of vibrations of black holes.The main motivation to study the QNMs of a black hole is twofold: One is to answer the question of whether or not the spacetime is stable, and the other to know what kind of oscillations will be excited in the spacetime when some perturbations are given. From an astrophysical point of view, the latter is quite important from the observational point of view because we could determine the fundamental parameters of a black hole, such as the mass or the angular momentum, through the information of the QNMs. QNMs have also been used for testing general relativity. In this Thesis,we will first consider the Schwartzchild Black holes in the ”normal” polar coordinates as a test case and calculate the QNMs due to scalar and Electromagnetic perturbations. Then we will be considering the Schwartzchild De Sitter(SDS) Black holes in the ”normal” polar coordinates. SdS spacetime has no spatial infinity but has a cosmological horizon, it will be interesting to see the impact of this cosmological horizon in addition to the Event Horizon of the Black Hole on the QNMs.Furthermore, recent observations show that the universe does have a nonzero positive cosmological constant. Therefore, SdS spacetimes are considered to be a good simple model of a black hole in the universe. After procuring the appropriate boundary conditions from either the tortoise coordinates or by approaximating solutions, we constructed a proper series solution with suitable prefactors such that the boundary condiations could be simultaneously be satisfied.From there the relevant recursion relations were obtained which were used to derive the continued fraction equation. Solution the said equations are the desired Quasinormal modes.

Actions (login required)

View Item