On the critical behaviour of gapped gravitational collapse in confined spacetime

TL;DR

This paper studies the critical behavior of gapped gravitational collapse in a confined spacetime with a cosmological constant, revealing new scaling laws and how critical exponents depend on the spacetime parameters.

Contribution

It introduces new time and mass scaling laws for gapped collapse and shows how critical exponents vary with the cosmological constant and boundary conditions.

Findings

Confirmed the mass scaling law for gapped collapse.

Discovered a new time scaling law for gapped collapse.

Critical exponents depend on the combination of cosmological constant and boundary radius.

Abstract

The gravitational collapse of a massless scalar field enclosed with a perfectly reflecting wall in a spacetime with a cosmological constant $\Lambda$ is investigated. The mass scaling for the gapped collapse $ M_{AH}-M_g \propto (\epsilon_c-\epsilon)^\xi$ is confirmed and a new time scaling for the gapped collapse $T_{AH}-T_g\propto(\epsilon_c-\epsilon)^\zeta$ is found. We find that both of these two critical exponents depend on the combination $\Lambda R^2$, where $R$ is the radial position of the reflecting wall. Especially, we find an evolution of the critical exponent $\xi$ from $0.37$ in the confined asymptotic dS case with $\Lambda R^2=1.5$ to $0.7$ in asymptotic AdS case ($\Lambda R^2\rightarrow-\infty$), while the critical exponent $\zeta$ varies from $0.10$ to $0.26$, which shows the new critical behavior for the gapped collapse is essentially different from the one in the Choptuik's case.