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

Abstract

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{approx_equal}M{sup 2}xK{sup 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 aremore » 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.« less

Authors:
 [1]
  1. Advanced Research Institute for Science and Engineering, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555 (Japan)
Publication Date:
OSTI Identifier:
20774689
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 73; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.73.104004; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COSMIC DUST; COSMOLOGICAL CONSTANT; COSMOLOGY; DE SITTER GROUP; GENERAL RELATIVITY THEORY; GRAVITATION; GRAVITATIONAL COLLAPSE; IDEAL FLOW; MATHEMATICAL SOLUTIONS; QUANTUM GRAVITY; SINGULARITY; SPACE-TIME; SURFACES; TRAPPING

Citation Formats

Maeda, Hideki. Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.104004.
Maeda, Hideki. Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. United States. doi:10.1103/PhysRevD.73.104004.
Maeda, Hideki. Mon . "Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity". United States. doi:10.1103/PhysRevD.73.104004.
@article{osti_20774689,
title = {Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity},
author = {Maeda, Hideki},
abstractNote = {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{approx_equal}M{sup 2}xK{sup 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.},
doi = {10.1103/PhysRevD.73.104004},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 73,
place = {United States},
year = {2006},
month = {5}
}