Black holes sourced by a massless scalar

Understand

We construct asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a nontrivial scalar field with 1/r asymptotic behaviour.

• Near the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution.
• The hairy black hole solutions allow for a consistent thermodynamical description.
• At large mass they have the same thermodynamical behaviour of the Schwarzschild black hole, whereas for small masses they differ substantially from the latter.