  Studying the gravitational collapse of dust particles toward newly formed
black holes has gained popularity following the observation of gravitational
waves resulting from the merger of black holes. In this paper, we focus on
modelling the descent of dust debris toward a black hole using a numerical code
that incorporates relativistic hydrodynamics in the framework of General and
Einstein-Gauss Bonnet gravity. We explore the influence of various parameters,
such as the black hole's rotation parameter a and the EGB coupling constant
alpha, on the curvature effects observed. Both parameters significantly impact
the dynamics of the accretion disk formed around the black holes. Furthermore,
we discuss the gravitational collapsing process in two distinct scenarios. It
is also observed that the mass accretion rate is significantly influenced by
these two parameters. The rate at which mass is accreted toward a black hole
directly impacts the black hole's growth and evolutionary trajectory.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology