On metric independent perturbation scheme and associated relativistic acoustic geometry for spherical accretion

Abstract

Stationary solutions of the fluid dynamic equations governing the infall of matter on compact astrophysical objects have widely been studied by the accretion astrophysicists to probe the nature of the emitted spectra through which one can make predictions about the observational evidences of the black holes in our universe. To have a better understanding of the accretion process, one, however, needs to ensure that such stationary states are stable, and very few works, that too on case by case basis, are available in the literature which provide any comprehensive scheme of the stability analysis of the stationary accretion solutions in curved space time. A linear perturbation analysis of the steady state solutions of the Euler and the continuity equations has been developed in this thesis which works for any space time metric, and hence is sufficiently general to incorporate the stability analysis of non-dissipative continuous medium within a metric independent framework. The aim of this thesis is to show that a generalized linear perturbation scheme, independent of the mode of perturbation can be developed for any general relativistic spherically symmetric static space time which not only ensures the stability of the integral stationary accretion solutions but also leads to the emergence of a relativistic acoustic metric representing a curved manifold. The work presented in this thesis is a part of the ongoing project. The main project has been developed to study, along with the linear perturbation scheme in spherically symmetric static space time, the onset and propagation of any generalized non-linear perturbation in any general stationary axisymmetric space time, even for space time endowed with spin and the cosmological constant, and to investigate the corresponding emergent gravity phenomena. The content of this thesis will be submitted as a manuscript, along with two other manuscripts (under preparation) where all the findings of the aforementioned long term project will be reported.