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

Abstract

In this paper, we study spherical gravitational collapse of inhomogeneous pressureless matter in a well-defined $n\to 4$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.

25 pages, 22 figures