Abstract:
This thesis investigates the theoretical framework of spherically symmetric perfect
fluid spheres within the realm of general relativity. Our work seeks exact solutions to the
Einstein field equations thereby facilitating a better knowledge of minuscule objects. The
thesis begins by examining the fundamental aspects of special relativity, including the
Lorentz transformations and the structure of spacetime. We then explore general relativity,
with an eye towards the Einstein field equations and the geometric justification of gravity.
Examining matter dispersion in astrophysical systems depends on first looking at the
behavior of ideal fluids.
The thesis delves into the intricacies of the Einstein field equations and their application
to spacetimes with spherical symmetry. The key achievement of the research is the
formulation of new exact solutions for static spherically symmetric ideal fluid spheres.
Implementing two techniques in the context of static spherically symmetric ideal fluid line
elements, we develop two new approaches that validate their characteristics and ensure
that they satisfy Buchdhal criteria.
The physical characteristics and possible astrophysical implications of these solutions are
thoroughly investigated. Combining the ideas of general relativity with the simplified
model of perfect fluids helps this work provide new understanding on the interactions
between compact objects and their gravitational interactions.
