### Abstract

We investigate the stability of black hole solutions in an effective theory derived from a superstring model, which includes a dilaton field and the Gauss-Bonnet term. The critical solution, below which mass no static solution exists, divides a family of solutions in the mass-entropy diagram into two. The upper branch approaches the Schwarzschild solution in the large mass limit, while the lower branch ends up with a singular solution which has a naked singularity. In order to investigate the stability of black hole solutions, we adopt two methods. The first one is catastrophe theory, with which we discuss the stability of non-Abel an black holes in general relativity. The present system is classified as a fold catastrophe, which is the simplest case. Following catastrophe theory, if we regard entropy and mass as the potential and the control parameter, respectively, we find the lower branch is more unstable than the upper branch. To confirm this, we study the second method, which is a linear perturbation analysis. We find an unstable mode only for the solutions in the lower branch. Hence, our investigation presents one example that catastrophe theory is also applicable for a generalized theory of gravity.

Original language | English |
---|---|

Article number | 084004 |

Pages (from-to) | 840041-8400413 |

Number of pages | 7560373 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 58 |

Issue number | 8 |

Publication status | Published - 1998 Oct 15 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*58*(8), 840041-8400413. [084004].

**Stability of a dilatonic black hole with a Gauss-Bonnet term.** / Torii, Takashi; Maeda, Keiichi.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 58, no. 8, 084004, pp. 840041-8400413.

}

TY - JOUR

T1 - Stability of a dilatonic black hole with a Gauss-Bonnet term

AU - Torii, Takashi

AU - Maeda, Keiichi

PY - 1998/10/15

Y1 - 1998/10/15

N2 - We investigate the stability of black hole solutions in an effective theory derived from a superstring model, which includes a dilaton field and the Gauss-Bonnet term. The critical solution, below which mass no static solution exists, divides a family of solutions in the mass-entropy diagram into two. The upper branch approaches the Schwarzschild solution in the large mass limit, while the lower branch ends up with a singular solution which has a naked singularity. In order to investigate the stability of black hole solutions, we adopt two methods. The first one is catastrophe theory, with which we discuss the stability of non-Abel an black holes in general relativity. The present system is classified as a fold catastrophe, which is the simplest case. Following catastrophe theory, if we regard entropy and mass as the potential and the control parameter, respectively, we find the lower branch is more unstable than the upper branch. To confirm this, we study the second method, which is a linear perturbation analysis. We find an unstable mode only for the solutions in the lower branch. Hence, our investigation presents one example that catastrophe theory is also applicable for a generalized theory of gravity.

AB - We investigate the stability of black hole solutions in an effective theory derived from a superstring model, which includes a dilaton field and the Gauss-Bonnet term. The critical solution, below which mass no static solution exists, divides a family of solutions in the mass-entropy diagram into two. The upper branch approaches the Schwarzschild solution in the large mass limit, while the lower branch ends up with a singular solution which has a naked singularity. In order to investigate the stability of black hole solutions, we adopt two methods. The first one is catastrophe theory, with which we discuss the stability of non-Abel an black holes in general relativity. The present system is classified as a fold catastrophe, which is the simplest case. Following catastrophe theory, if we regard entropy and mass as the potential and the control parameter, respectively, we find the lower branch is more unstable than the upper branch. To confirm this, we study the second method, which is a linear perturbation analysis. We find an unstable mode only for the solutions in the lower branch. Hence, our investigation presents one example that catastrophe theory is also applicable for a generalized theory of gravity.

UR - http://www.scopus.com/inward/record.url?scp=0542418281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0542418281&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0542418281

VL - 58

SP - 840041

EP - 8400413

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

M1 - 084004

ER -