Spherical Gravitational Collapse in 4D Einstein-Gauss-Bonnet theory

TL;DR

This paper investigates how spherical gravitational collapse in 4D Einstein-Gauss-Bonnet gravity can result in either black holes or naked singularities, showing that the theory generally violates cosmic censorship depending on initial conditions and coupling strength.

Contribution

It provides a detailed analysis of collapse outcomes in 4D Einstein-Gauss-Bonnet gravity, revealing conditions under which naked singularities can form, thus challenging cosmic censorship.

Findings

Naked singularities form if initial conditions satisfy F(r,t)< 2√λ.

Black holes form when F(r,t)≥ 2√λ, with horizons developing accordingly.

The theory generally violates cosmic censorship in 4D Einstein-Gauss-Bonnet gravity.

Abstract

In this paper, we study spherical gravitational collapse of inhomogeneous pressureless matter in a well-defined $n \rightarrow4$d limit of the Einstein-Gauss-Bonnet gravity. The collapse leads to either a black hole or a massive naked singularity depending on time of formation of trapped surfaces. More precisely, horizon formation and its time development is controlled by relative strengths of the Gauss-Bonnet coupling $(\lambda)$ and the Misner-Sharp mass function $F(r,t)$ of collapsing sphere. We find that, if there is no trapped surfaces on the initial Cauchy hypersurface and $F(r,t)< 2\sqrt{\lambda}$, the central singularity is massive and naked. When this inequality is equalised or reversed, the central singularity is always censored by spacelike/timelike spherical marginally trapped surface of topology $S^{2}\times \mathbb{R}$, which eventually becomes null and coincides with the event horizon at equilibrium. These conclusions are verified for a wide class of mass profiles admitting different initial velocity conditions. Hence, our result implies that the $4$d Einstein-Gauss-Bonnet generically violates the cosmic censorship conjuncture. Further implications of this violation from the perspective of visibility of causal signals from the spacetime singularity are also discussed.