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

Synopsis

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 the solution with a non-stealth scalar field obtained by Xu in a mush simpler coordinate system. We show that different domains of coordinates of the last solution represent distinct spacetimes. One of them is the maximal extension of the Xu's spacetime and represents a shrinking black hole. Another spacetime can be attached to the past AdS spacetime in a regular manner and then the whole spacetime represents the gravitational collapse from regular initial data. It is shown that the resulting singularity is censored and the spacetime represents the formation of a black hole under an assumption for future-directed radial null geodesics, but the proof without the assumption is left open.