On the critical behaviour of gapped gravitational collapse in confined spacetime

Abstract

The gravitational collapse of a massless scalar field enclosed with a perfectly reflecting wall in a spacetime with a cosmological constant $Λ$ is investigated. The mass scaling for the gapped collapse $ M_{AH}-M_g \propto (ε_c-ε)^ξ$ is confirmed and a new time scaling for the gapped collapse $T_{AH}-T_g\propto(ε_c-ε)^ζ$ is found. We find that both of these two critical exponents depend on the combination $ΛR^2$, where $R$ is the radial position of the reflecting wall. Especially, we find an evolution of the critical exponent $ξ$ from $0.37$ in the confined asymptotic dS case with $ΛR^2=1.5$ to $0.7$ in asymptotic AdS case ($ΛR^2\rightarrow-\infty$), while the critical exponent $ζ$ 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.