On the Critical Behavior of Gapped Gravitational Collapse in Confined Spacetime**Supported in part by the National Natural Science Foundation of China under Grant Nos. 11375247 and 11435006, and a Key Project of CAS, under Grant No. QYZDJ-SSW-SYS006

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 is confirmed and a new time scaling for the gapped collapse is found. For both the critical exponents, we find strong evidence to show that they are non-universal. Especially when , we find that both of these two critical exponents depend on the combination , where R is the radial position of the reflecting wall. We find an evolution of the critical exponent ξ from 0.37 in the confined asymptotic dS case with to 0.68 in the confined asymptotic AdS case with , while the critical exponent ζ varies from 0.10 to 0.26, which shows that the new critical behavior for the gapped collapse is essentially different from the Choptuik’s case.