Tipler Naked Singularities in Dimensions
arXiv:2404.02940 · doi:10.1088/1361-6382/ad6115
Abstract
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if at least one of these causal geodesics is past incomplete. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I matter fields in an arbitrarily finite number of dimensions. In the spirit of Joshi and Dwivedi [26], and Goswami and Joshi [31], we first construct regular initial data in terms of matter variables and geometric quantities, subject to the dominant and null energy conditions. Using this initial data, we derive two distinct (but not mutually exclusive) conditions, which we call the positive root condition (PRC) and the simple positive root condition (SPRC), that serve as necessary and sufficient conditions, respectively, for the existence of naked singularities. In doing so, we generalize the results of [26] and [31]. We further restrict the PRC and the SPRC by imposing the curvature growth condition (CGC) of Clarke and Krolak [24] on all causal curves that satisfy the causal convergence condition. The CGC gives a sufficient condition for the naked singularities implying the PRC and implied by the SPRC, to be of strong curvature type; thereby also implying the inextendibility of the spacetime. Using the CGC, we extend the results of [28] (that hold for dimension ) to the case , showing that strong curvature naked singularities can occur in this case. However, for the case , we show that past-incomplete causal curves that identify naked singularities do not satisfy the CGC. These results shed light on the validity of the cosmic censorship conjectures in arbitrary dimensions.
Corrections about regularity class of inextendibility added
References in corpus (29)
- The Dynamics of General Relativity
- Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification
- Black Holes in Higher Dimensions
- Singularity Theorems and Their Consequences
- Kerr-AdS/CFT Correspondence in Diverse Dimensions
- Equilibrium configurations from gravitational collapse
- Quantum evaporation of a naked singularity
- Spherical gravitational collapse in N-dimensions
- Thermodynamics of higher dimensional black holes with higher order thermal fluctuations
- Higher-dimensional origin of extended black hole thermodynamics
- Naked Singularities in Higher Dimensional Gravitational Collapse
- On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification
- Growing Extra Dimensions in AdS/CFT
- Strong curvature naked singularities in spherically symmetric perfect fluid collapse
- Gravitational collapse of an isentropic perfect fluid with a linear equation of state
- Cosmic Censorship in Higher Dimensions
- Dynamical extensions for shell-crossing singularities
- Stability and gravitational collapse of neutron stars with realistic equations of state
- Is cosmic censorship restored in higher dimensions?
- The singularity theorems of General Relativity and their low regularity extensions
- New mathematical framework for spherical gravitational collapse
- Packing extra mass in compact stellar structures: An interplay between Kalb-Ramond field and extra dimensions
- Stability and phase transition of rotating Kaluza-Klein black holes
- Cosmic Censorship in Higher dimension II
- Asymptotic flatness and Hawking quasilocal mass
- Shell-crossings in Gravitational Collapse
- Entropy-current for dynamical black holes in Chern-Simons theories of gravity
- Black hole regions containing no trapped surfaces
- Dimensional dependence of naked singularity formation in spherical gravitational collapse