Inhomogeneous dust collapse in 5D Einstein-Gauss-Bonnet gravity

We consider a Lemaitre-Tolman-Bondi type space-time in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms, and present an exact solution in closed form. It turns out that the presence of the coupling constant of the Gauss-Bonnet terms $\alpha >0$ completely changes the causal structure of the singularities from the analogous general relativistic case. The gravitational collapse of inhomogeneous dust in the five-dimensional Gauss-Bonnet extended Einstein equations leads to formation of a massive, but weak, timelike singularity which is forbidden in general relativity. Interestingly, this is a counterexample to three conjectures, viz., cosmic censorship conjecture, hoop conjecture, and Seifert’s conjecture.

Figure 1

A 2D picture of the EGB collapse showing formation of singularity and apparent horizon for the parameter values ${ϵ}_0=1$, $\alpha =0.2$, $r_b=5.5$. The dotted curves represent singularity, whereas the apparent horizons are the continuous ones.