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

Xuefeng Zhang; H. Lu

doi:10.1016/j.physletb.2014.07.052

paper

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

arXiv:1403.6874 · doi:10.1016/j.physletb.2014.07.052

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 $Λ$ in the potential. As the advanced time $u$ increases, the spacetime reaches equilibrium in an exponential fashion, i.e., $e^{- u / u_{0}}$ with $u_{0} \sim 1/ (α^{4} M_{0})^{1/3}$ , where $M_{0}$ is the mass of the final black hole and $α$ 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 $α = 0$ 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 $Λ \geq 0$ . For $Λ < 0$ , it can be instead used to study non-equilibrium thermalization of certain strongly-coupled field theory.

arXiv commentLatex, 8 pages, typos corrected and references added

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

Abstract

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