Exact black-hole formation with a conformally coupled scalar field in three dimensions

TL;DR

This paper derives exact solutions in three-dimensional AdS gravity with a conformally coupled scalar field, demonstrating black-hole formation from regular initial data and exploring various dynamical spacetime configurations.

Contribution

It provides the first exact inhomogeneous solutions showing black-hole formation with a conformally coupled scalar field in 3D AdS gravity.

Findings

Black-hole formation from regular initial data in AdS spacetime.

Existence of solutions with event horizons but no trapped surfaces.

Identification of dynamical black holes with asymptotic static behavior.

Abstract

We present exact dynamical and inhomogeneous solutions in three-dimensional AdS gravity with a conformally coupled scalar field. They contain stealth configurations of the scalar field overflying the BTZ spacetime and also solutions with a non-vanishing energy-momentum tensor. The latter non-stealth class consists of the solution obtained by Xu and its analytic extension. It is shown that this proper extension represents: (i) an eternally shrinking dynamical black hole, (ii) a curious spacetime which admits an event horizon without any trapped surface, or (iii) gravitational collapse of a scalar field in an asymptotically AdS spacetime. In the last case, by attaching the solution regularly to the past massless BTZ spacetime with a vanishing scalar field, the whole spacetime represents the black-hole formation from regular initial data in an asymptotically AdS spacetime. Depending on the parameters, the formed black hole can be asymptotically static in far future.