Perturbations of Time-Dependent Gravitational Systems

Author(s)

Carlos Eduardo Pellicer de Oliveira

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2007-06-13

Examining board members

Elcio Abdalla; Frank Michael Forger; Alberto Vazquez Saa

• Advisor: Elcio Abdalla

Abstract

This work is a study on the time evolution of scalar perturbations around a star collapsing to a black hole. It starts with a basic study of gravitation and quasi-normal modes. The aim is to derive the solution of the massless Klein-Gordon equation, that depends on numerical methods. Aiming at this goal, we studied theoretical aspects of stars, black holes and gravitational collapse. The methods include coordinate substitutions to modify the Klein-Gordon equation to a simple form. We also studied numerical methods for partial differential equations. Solutions of the quasi-normal modes were found with different values of M, R and l. The solutions are irregular in several situations, but some of them display increasing modes, that could be explained by the explosive behavior of Supernovas. (AU)