Scalar collapse in AdS spacetimes

Abstract

Recently, studies of the gravitational collapse of a scalar field within spherically symmetric anti--de Sitter (AdS) spacetimes presented by Bizon and Rostroworoski [Phys. Rev. Lett. 107, 031102 (2011)], Jalmuzna et al. [Phys. Rev. D 84, 085021 (2011).] showed an instability of pure AdS to black hole formation. In particular, the work showed that arbitrarily small initial configurations of a scalar field evolved through some number of reflections off the AdS boundary until a black hole forms. We consider this same system, extended to include a complex scalar field, and reproduce this phenomena. We present tests of our numerical code that demonstrate convergence and consistency. We study the properties of the evolution as the scalar pulse becomes more compact by examining the asymptotic behavior of the scalar field, an observable in the corresponding boundary conformal field theory. We demonstrate that such black hole formation occurs even when one places a reflecting boundary at finite radius, indicating that the sharpening is a property of gravity in a bounded domain and not of AdS itself. We examine how the initial energy is transferred to higher frequencies---which leads to black hole formation---and uncover interesting features of this transfer.