Moving Closer to the Collapse of a Massless Scalar Field in Spherically Symmetric Anti-de Sitter Spacetimes

TL;DR

This paper introduces a hybrid evolution method combining Cauchy and characteristic techniques to study gravitational collapse of massless scalar fields in spherically symmetric Anti-de Sitter spacetimes, providing new numerical insights.

Contribution

The paper develops a novel hybrid evolution scheme that effectively tracks scalar fields near horizon formation in AdS, enhancing numerical analysis of gravitational collapse.

Findings

Numerical evidence supporting a power-law scaling of the apparent horizon mass.

Computed critical exponents and echoing periods consistent with asymptotically-flat cases.

Improved numerical methods for studying near-horizon dynamics in AdS spacetimes.

Abstract

We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different bounces off the AdS boundary while the characteristic method can bring us very close to the point of formation of an apparent horizon. Here, we describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of massless scalar fields. We use this scheme to provide more numerical evidence for a recent conjecture on the power-law scaling of the apparent horizon mass resulting from the collapse of subcritical configurations. We also compute the critical exponents and echoing periods for a number of critical points and confirm the expectation that their values should be the same as in the asymptotically-flat case.