Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model

TL;DR

This paper provides an exact analytical model of critical gravitational collapse in 2+1 dimensional Anti-de Sitter spacetime, revealing a critical exponent of 2/5 and connecting to self-similar solutions.

Contribution

It introduces a new exact collapsing solution in 2+1 gravity with negative cosmological constant, advancing understanding of critical phenomena in lower-dimensional gravity.

Findings

Critical exponent γ = 2/5 identified.

Perturbations lead to approximate black hole solutions.

Global causal structure analyzed in relation to self-similarity.

Abstract

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the $\Lambda=0$ case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be $\gamma = 2/5$.