Exact Black Hole Formation in Asymptotically (A)dS and Flat Spacetimes

Abstract

We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a static scalar-hairy black hole. The solution can be asymptotically AdS, flat or dS depending on the value of the cosmological constant parameter $\Lambda$ in the potential. As the advanced time $u$ increases, the spacetime reaches equilibrium in an exponential fashion, i.e., $e^{-u/u_0}$ with $u_0\sim 1/({\alpha }^4{M}_0{)}^{1/3}$, where $M_0$ is the mass of the final black hole and $\alpha$ is the second parameter in the potential. Similar to the Vaidya solution, at $u=0$, the spacetime can be matched to an (A)dS or flat vacuum except that at the origin a naked singularity may occur. Moreover, a limiting case of our solution with $\alpha =0$ gives rise to an (A)dS generalization of the Roberts solution, thereby making it relevant to critical phenomena. Our results provide a new model for investigating formation of real life black holes with $\Lambda \ge 0$. For $\Lambda <0$, it can be instead used to study non-equilibrium thermalization of certain strongly-coupled field theory.

Latex, 8 pages, typos corrected and references added

References in corpus (2)

• Weak Field Black Hole Formation in Asymptotically AdS Spacetimes
• Exact Hairy Black Holes

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