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

We give a model of the gravitational collapse of a null dust fluid including the perturbative effects of quantum gravity. The $n (\geq 5)$-dimensional action with the Gauss-Bonnet terms for gravity is considered, and a general spherically symmetric solution is obtained. We consider the situation in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity inevitably forms. In the $n \ge 6$ case, an ingoing null naked singularity forms, while in the $n=5$ case, a massive timelike naked singularity forms, which does not appear in the general relativistic case. The strength of the naked singularities is weaker than the strength of 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 empty asymptotically flat spacetime.