Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n(>=5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M[approximate]M²×K^n-2 with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n>=6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n>=6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n>=6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n>=6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n>=10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5<=n<=8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.

©2006 The American Physical Society