Black Hole Formation In The Context Of General Relativity And Modified Theory Of Gravity

In the last three to four decades,several programs have been studied in order to investigate the final fate of gravitational collapse of massive astrophysical objects.In the theoretical context,black holes are the consequences of final fate of gravitational collapse.In this thesis,firstly we provide the basic of Einstein’s theory of gravity in 4-dimensional spacetimes.After that,we applied the developed fundamental formulae and study the spherical symmetric clump of matter made up of dark matter ρM in the presence of dark energy p.It is investigated that gravitational collapse of dark matter combination with dark energy leads to the formation of black hole.When l+ 2k<-3(phantoms),dust and phantoms could be ejected from the death of white whole.This emitted matter again undergoes to collapsing process and become the black hole.In second chapter,we consider the full general relativistic treatment of the underlying problem and obtain exact solutions for different types of the equation of state(l,k):pt = kρ and pr = lρ,(l+2k)<-1 connecting the tangential and radial pressure respectively.In chapter 3,we extended results from general relativity to modified theory of gravity i.e.,brane-worlds scenario.Gravitational collapse of spherical symmetric star is discussed in the context of brane-worlds scenario.In this chapter,anisotropy in pressure in a fluid is discussed with equation of state pt = kp and pr = lp,((l + 2k)<-1).We briefly discusse various cases of gravitational collapsing process i.e.,a)collapse of dark matter only,b)collapse with dark energy only,c)collapse of non-interacting combination of dark matter and dark energy i.e.,Q = 0(Q is an interaction term)and in the last case,d)collapsing process of interacting combination of dark matter and dark energy i.e.,Q ≠ 0.It is found that a black hole can be formed by the gravitational collapse in brane-worlds regime while in some cases there is only a naked singularity at their end state.In chapter 4,we investigate the gravitational collapse of spherically symmetric gravitational bound object which is made of dust cloud interacting xxwith the growing vacuum energy density A(t)(time varying vacuum energy density).This vacuum en-ergy density is represented by the parameters 3 in the recent research study.The con-cept of a pressure anisotropy in stellar models is produced by a large set of physical phenomena in high density regimes.We consider a gravitational collapse process of the anisotropic fluid interacting with a growing vacuum energy density and provide the results of final fates of gravitational collapse.We consider the full general-relativistic treatment of this problem and obtain exact solutions for various forms of the equation of state(k,l):pt＝kρ and pr=lp,(l + 2k)<-1 connecting the tangential and radial pressures respectively.