Naked singularities in higher dimensional Szekeres space–time

Abstract

In this paper we study the quasi-spherical gravitational collapse of (n + 2)-dimensional Szekeres space-time. The nature of the central shell focusing singularity so formed is analyzed by studying both the radial null and time-like geodesic originated from it. We follow the approach of Barve et al to analyze the null geodesic and find naked singularity in different situations.

Quasispherical gravitational collapse in 5D Einstein-Gauss-Bonnet gravity

“…We call the family that has the minus (plus) sign the minus (plus) branch solution. In the general relativistic limit α → 0, we recover the 5D-QSZ solution in Einstein gravity [9,10]. Maeda [29] has analyzed LTB models near center (r ∼ 0) in EGB and pointed out the occurrence of major changes in the final fate of collapse (see also, [28]).…”

“…It is easy to see that as α → 0 the master solution (16) of the system reduces to the corresponding 5D-QSZ solution in [9,10]…”

“…Therefore, the Szekeres spacetime is often called as quasispherical, for definiteness we shall name it as quasispherical Szekeres (QSZ) solutions. Being an exact model of the spacetime geometry, the QSZ solutions have primarily been adapted with regards to studies of nonspherical collapse of inhomogeneous dust cloud [1,[3][4][5][6][7][8] in four dimensions (4D), and in higher dimensions [9,10], in cosmology [11][12][13][14][15][16] and also in observational cosmology [17]. They are very important because they admit no Killing vectors [11] and hence they are lacking symmetry.…”

The Effect of Pressure in Higher Dimensional Quasi-Spherical Gravitational Collapse

“…Also in the perspective of black hole physics and its astrophysical implications, the end state of collapse (black hole or naked singularity) is interesting. As there exists no formal method to address this problem so it is natural to study various examples of collapsing system (namely, Tolman-Bondi-Lemaître (TBL) spherically symmetric model [6][7][8][9][10][11][12][13][14][15] or quasi-spherical Szekeres' model [16][17][18]) with a view to gain some insight. In general, these studies conclude that the local or global visibility of the central curvature singularity depends on the initial data.…”

Quasi-Spherical Gravitational Collapse in higher dimension and the effect of equation of state

“…Though a lot of works have been done for dust collapse [7][8][9][10][11][12] both for spherical and quasi-spherical models [13][14][15][16][17][18] in four and higher dimensional space-times but there is not much progress in studying gravitational collapse in quasi-spherical space for perfect fluid or matter with anisotropic pressure [19]. In recent past Dadhich etal [20] examined the role of the equation of state in charecterizing the final state of spherical collapse and showed a similarity among collapsing processes in different dimensions with different eq.…”