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Title: Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case

Abstract

We have studied spacetime structures of static solutions in the n-dimensional Einstein-Gauss-Bonnet-Maxwell-{lambda} system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient {alpha} is non-negative and 4{alpha}-tilde/l{sup 2}{<=}1 in order to define the relevant vacuum state. Solutions have the (n-2)-dimensional Euclidean submanifold whose curvature is k=1, 0, or -1. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of a spacetime. A branch singularity appears at the finite radius r=r{sub b}>0 for any mass parameter. There the Kretschmann invariant behaves as O((r-r{sub b}){sup -3}), which is much milder than the divergent behavior of the central singularity in general relativity O(r{sup -4(n-2)}). In the k=1 and 0 cases plus-branch solutions have no horizon. In the k=-1 case, the radius of a horizon is restricted as r{sub h}<{radical}(2{alpha}-tilde) (r{sub h}>{radical}(2{alpha}-tilde) in the plus (minus) branch. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. There are topological black hole solutions with zero and negative mass in the plus branch regardless of the sign ofmore » the cosmological constant. Although there is a maximum mass for black hole solutions in the plus branch for k=-1 in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with k=-1 and n{>=}6 have an inner black hole and inner and outer black hole horizons. In the 4{alpha}-tilde/l{sup 2}=1 case, only a positive mass solution is allowed, otherwise the metric function takes a complex value. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.« less

Authors:
 [1];  [2]
  1. Graduate School of Science, Waseda University, Shinjuku-ku, Tokyo 169-8555 (Japan)
  2. Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555 (Japan)
Publication Date:
OSTI Identifier:
20713540
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.72.064007; (c) 2005 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; BLACK HOLES; COSMOLOGICAL CONSTANT; COSMOLOGY; EUCLIDEAN SPACE; GENERAL RELATIVITY THEORY; GRAVITATION; MATHEMATICAL SOLUTIONS; NEGATIVE MASS; SINGULARITY; SPACE-TIME; TOPOLOGY; VACUUM STATES

Citation Formats

Torii, Takashi, Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, and Maeda, Hideki. Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.064007.
Torii, Takashi, Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, & Maeda, Hideki. Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case. United States. doi:10.1103/PhysRevD.72.064007.
Torii, Takashi, Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555, and Maeda, Hideki. Thu . "Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case". United States. doi:10.1103/PhysRevD.72.064007.
@article{osti_20713540,
title = {Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case},
author = {Torii, Takashi and Advanced Research Institute for Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555 and Maeda, Hideki},
abstractNote = {We have studied spacetime structures of static solutions in the n-dimensional Einstein-Gauss-Bonnet-Maxwell-{lambda} system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient {alpha} is non-negative and 4{alpha}-tilde/l{sup 2}{<=}1 in order to define the relevant vacuum state. Solutions have the (n-2)-dimensional Euclidean submanifold whose curvature is k=1, 0, or -1. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of a spacetime. A branch singularity appears at the finite radius r=r{sub b}>0 for any mass parameter. There the Kretschmann invariant behaves as O((r-r{sub b}){sup -3}), which is much milder than the divergent behavior of the central singularity in general relativity O(r{sup -4(n-2)}). In the k=1 and 0 cases plus-branch solutions have no horizon. In the k=-1 case, the radius of a horizon is restricted as r{sub h}<{radical}(2{alpha}-tilde) (r{sub h}>{radical}(2{alpha}-tilde) in the plus (minus) branch. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. There are topological black hole solutions with zero and negative mass in the plus branch regardless of the sign of the cosmological constant. Although there is a maximum mass for black hole solutions in the plus branch for k=-1 in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with k=-1 and n{>=}6 have an inner black hole and inner and outer black hole horizons. In the 4{alpha}-tilde/l{sup 2}=1 case, only a positive mass solution is allowed, otherwise the metric function takes a complex value. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.},
doi = {10.1103/PhysRevD.72.064007},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 72,
place = {United States},
year = {2005},
month = {9}
}