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

Understand

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 $u_0\sim1/(\alpha^4 M_0)^{1/3}$, where $M_0$ is the mass of the final black hole and $\alpha$ is the second parameter in the potential.