New look at AdS black holes with conformal scalar hair (2403.18048v3)
Abstract: We revisit static, spherically symmetric solutions to AdS-Einstein gravity with a conformally coupled scalar field (and no self-interaction potential) in four dimensions. We first observe that a convenient choice of coordinates leads to a significant simplification of the field equations, which enables one to identify various roots of the indicial equations and thus distinct branches of solutions. Next, we construct an explicit 2-parameter hairy black hole solution in terms of an infinite power series around the event horizon. The black hole is non-extremal with a regular scalar field on and outside the event horizon, and it reduces to the Schwarzschild-AdS metric in the limit of vanishing hair. Its properties are illustrated for various values of the parameters and compared with previous numerical results by other authors. In addition, the analysis reveals the presence of a photon sphere and how the scalar field affects its size and the angular radius of the corresponding shadow. The thermodynamics of the solution is also briefly discussed.
- M. Heusler, Black Hole Uniqueness Theorems. Cambridge University Press, Cambridge, 1996.
- gr-qc/9605059.
- 1601.08230.
- S. Ray. To appear.
- R. M. Wald, General Relativity. The University of Chicago Press, Chicago, 1984.
- Cambridge University Press, Cambridge, second ed., 2003.
- Cambridge University Press, Cambridge, 1986.
- H. Piaggio, An Elementary Treatise on Differential Equations and their Applications. G. Bell and sons, Ltd., London, 1920.
- W. Rudin, Principles of Mathematical Analysis. McGraw-Hill, New York, third ed., 1976.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.