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

Physical Review D (Impact Factor: 4.64). 02/2006; 73(10). DOI: 10.1103/PhysRevD.73.104004
Source: arXiv


We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime $M \approx M^2 \times K^{n-2}$ 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 $n \ge 6$. There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for $n \ge 6$, 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. In the minus-branch solution, naked singularities are massless for $n \ge 6$, 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 $n \ge 6$, while it is ingoing-null for $n=5$. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for $n \ge 10$ and for $n=9$ depending on the parameters in the initial data, while a naked singularity is always formed for $5 \le n \le 8$. 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. Comment: 23 pages, 1 figure, final version to appear in Physical Review D

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    • "There are earlier works considering its status, and there seems to be a consensus towards the idea that naked singularities can be produced via gravitational collapse in Lovelock theory. For instance, the case of LGB gravity without cosmological constant has been analyzed, both for the spherically symmetric gravitational collapse of a null dust fluid that generalizes Vaidya's solution [26] and for that of a perfect fluid dust cloud [27]. Some particular cases of Lovelock gravity have been considered as well; namely, so-called dimensionally continued gravity [28] and cubic Lovelock theory [29]. "
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