The dimensional dependence of naked singularity formation in spherical gravitational collapse

Abstract

The complete spectrum of the endstates -naked singularities, or blackholes -of gravitational collapse is analyzed for a wide class of N -dimensional spacetimes in spherical symmetry, which includes and generalizes the dust solutions and the case of vanishing radial stresses. The final fate of the collapse is shown to be fully determined by the local behavior of a single scalar function and by the dimension N of the spacetime. In particular, the "critical" behavior of the N = 4 spacetimes, where a sort of phase transition from black hole to naked singularity can occur, is still present if N = 5 but does not occur if N > 5, independently from the initial data of the collapse. Physically, the results turn out to be related to the kinematical properties of the considered solutions.

Gravitational Collapse in the EGB Gravity

“…Thirdly, few regularity conditions on the metric functions must also be enforced during the collapse process. The positivity and regularity of the density ρ(t, r), and equation (9) imply that the mass function F (t, r) must smoothly vanish at the center of the matter configuration at r = 0. The condition R(t, r) = 0 is the genuine spacetime singularity where the density and the curvature scalars blow up.…”

“…The models of gravitational collapse in alternate theories of gravity, including higher dimensional ones, are also being studied with interest since it is believed that one (or some) of these theories may solve problems affecting GR, including spacetime singularities [7,8,9,10,11,12,13]. Among these, modified gravity theories with higher curvature corrections arise naturally.…”

“…Thus, because of importance of the EGB theory as a natural higher dimensional theory, effect of the GB correction term on the spherically symmetric gravitational collapse and singularity structure have received attention. Naturally, particular emphasis has been placed on the inhomogenous dust collapse models of Lemaitre-Tolman-Bondi (LTB) type [7,8,9,10,11]. In particular, [7] has carried out a complete study of the singularity structure of all the collapse models for spacetime dimensions n ≥ 5.…”

Tipler naked singularities in N dimensions

“…Goswami and Joshi developed the formalism to study the gravitational collapse of spherically symmetric type-I matter field in higher dimensions [31] and showed the existence of naked singularities. Moreover, Giambo and Quintavalle [32] have investigated how the dimension of a spacetime affects the existence of a 'phase transition' 9 However, the strength of such singularities (in the sense of Tipler) has not been examined [33][34][35][36][37]. (iii) It may be interesting to assess the validity of the cosmic censorship conjectures in higher dimensions.…”

Null Fluid Collapse in Rastall Theory of Gravity

“…Consequently, causal curves terminating in the past at the singularity have the chance to reach the faraway observers thus exposing super-dense regions of extreme gravity to the external universe. [10,11] In this context, formation of naked singularities as collapse outcome has been studied within many different scenarios such as gravitational collapse of a dust cloud, [12] scalar fields' collapse, [13][14][15][16][17][18][19] gravitational collapse in higher dimensions [20][21][22][23][24][25][26] etc. (for a review see refs.…”