Effects of Gauss-Bonnet term on final fate of gravitational collapse

Abstract

We obtain a general spherically symmetric solution of a null dust fluid in n(⩾ 5)- dimensions in Gauss-Bonnet gravity. Using the solution for n ⩾ 5 with a specific form of the mass function, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed and its properties are quite different between n = 5 and n ⩾ 6. In the n ⩾ 6 case, a massless ingoing null naked singularity is formed, while in the n = 5 case, a massive timelike naked singularity is formed, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than that in the general relativistic case. These naked singularities can be globally naked when the null dust fluid is turned off after a finite time and the field settles into the empty asymptotically flat spacetime.