1998/09/09 by Takashi Torii, T. Torii, Kengo Maeda +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1103/physrevd.59.064027
published as Phys.Rev. D59 (1999) 064027 · 9 pages, 2 Postscript figures
arxiv created 1998/09/09 · openalex publication_date 1999/02/17 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.