Abstract
Gravitational collapse is the process by which an astronomical object, such as
a cloud of gas or a star, contracts under the influence of its own gravity. This
occurs when internal pressure becomes insufficient to counteract the inward
gravitational pull, leading to a continual contraction of matter toward the
center. In this dissertation, we study the formation of a black hole as a natural
consequence of gravitational collapse.
Firstly, we review the analytical solutions presented in the seminal work of
Oppenheimer and Snyder, “On Continued Gravitational Contraction”
[1], by deriving and analyzing the corresponding Einstein field equations. Secondly,
to address the approximations inherent in the OS model, we investigate
the geodesic equations governing the motion of infalling matter to evaluate
the development of an event horizon and the approach toward singularity formation.
The analysis ensures a consistent physical description by smoothly
matching the interior Friedmann–Robertson–Walker (FRW)-like metric with
the exterior Schwarzschild metric at the boundary of the collapsing dust cloud.