### Abstract

We discuss the no-hair conjecture in the presence of a cosmological constant. For the first step the real scalar field is considered as the matter field and the spacetime is assumed to be static spherically symmetric. If the scalar field is massless or has a convex potential such as a mass term, it is proved that there is no regular black hole solution. For a general positive potential, we search for black hole solutions which support the scalar field with a double well potential, and find them by numerical calculations. The existence of such solutions depends on the values of the vacuum expectation value and the self-coupling constant of the scalar field. When we take the zero horizon radius limit, the solution becomes a boson star like solution which we found before. However new solutions are found to be unstable against the linear perturbation. As a result we can conclude that the no-scalar-hair conjecture holds in the case of scalar fields with a convex or double well potential.

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

Pages (from-to) | 1-8 |

Number of pages | 8 |

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

Volume | 59 |

Issue number | 6 |

Publication status | Published - 1999 Mar 15 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

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

*59*(6), 1-8.

**Toward the no-scalar-hair conjecture in asymptotically de Sitter spacetime.** / Torii, Takashi; Maeda, Kengo; Narita, Makoto.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 59, no. 6, pp. 1-8.

}

TY - JOUR

T1 - Toward the no-scalar-hair conjecture in asymptotically de Sitter spacetime

AU - Torii, Takashi

AU - Maeda, Kengo

AU - Narita, Makoto

PY - 1999/3/15

Y1 - 1999/3/15

N2 - We discuss the no-hair conjecture in the presence of a cosmological constant. For the first step the real scalar field is considered as the matter field and the spacetime is assumed to be static spherically symmetric. If the scalar field is massless or has a convex potential such as a mass term, it is proved that there is no regular black hole solution. For a general positive potential, we search for black hole solutions which support the scalar field with a double well potential, and find them by numerical calculations. The existence of such solutions depends on the values of the vacuum expectation value and the self-coupling constant of the scalar field. When we take the zero horizon radius limit, the solution becomes a boson star like solution which we found before. However new solutions are found to be unstable against the linear perturbation. As a result we can conclude that the no-scalar-hair conjecture holds in the case of scalar fields with a convex or double well potential.

AB - We discuss the no-hair conjecture in the presence of a cosmological constant. For the first step the real scalar field is considered as the matter field and the spacetime is assumed to be static spherically symmetric. If the scalar field is massless or has a convex potential such as a mass term, it is proved that there is no regular black hole solution. For a general positive potential, we search for black hole solutions which support the scalar field with a double well potential, and find them by numerical calculations. The existence of such solutions depends on the values of the vacuum expectation value and the self-coupling constant of the scalar field. When we take the zero horizon radius limit, the solution becomes a boson star like solution which we found before. However new solutions are found to be unstable against the linear perturbation. As a result we can conclude that the no-scalar-hair conjecture holds in the case of scalar fields with a convex or double well potential.

UR - http://www.scopus.com/inward/record.url?scp=0007108696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007108696&partnerID=8YFLogxK

M3 - Article

VL - 59

SP - 1

EP - 8

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

ER -