Exploring the cosmic censorship conjecture with a Gauss-Bonnet sector

TL;DR

This paper investigates how Gauss-Bonnet corrections in a braneworld model modify black hole singularities during dust collapse, revealing conditions for naked sudden singularities to form.

Contribution

It demonstrates that Gauss-Bonnet effects can lead to a novel type of singularity with potential visibility, depending on model parameters.

Findings

Divergence of the Hubble rate derivative before singularity formation

Existence of a threshold mass for collapse leading to naked singularities

Modified singularity features due to Gauss-Bonnet curvature effects

Abstract

The Dvali-Gabadadze-Porrati (DGP) braneworld model is employed to study the gravitational collapse of dust, with a Gauss-Bonnet (GB) term present in the five-dimensional bulk. We find that, within the normal (nonself-accelerating) DGP branch and due to the curvature effects from the GB component on the brane, the black hole singularity acquires modified features. More precisely, during collapse and for a finite comoving time, before a singularity would emerge at the zero physical radius, the first time derivative of the Hubble rate diverges, whereas the brane energy density and the Hubble rate remain finite. This is a peculiar behavior which displays similar properties to the sudden singularity occurring in particular late-time cosmological frameworks. Furthermore, the question of whether this altered singularity can be viewed by an external observer or will be hidden by a black hole horizon is addressed. We establish that, depending on the given induced-gravity parameter and the GB coupling constant, there exists a {\em threshold mass} for the collapsing dust, below which no trapped surfaces evolve as the collapse proceeds toward the singularity. In other words, a {\em naked sudden singularity} may form.