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

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.