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.
