Interiors of Vaidya's radiating metric: Gravitational collapse

Abstract

Using the Darmois junction conditions, we give the necessary and sufficient conditions for the matching of a general spherically symmetric metric to a Vaidya radiating solution. We present also these conditions in terms of the physical quantities of the corresponding energy-momentum tensors. The physical interpretation of the results and their possible applications are studied, and we also perform a detailed analysis of previous work on the subject by other authors. PACS number(s1: 04.20.Jb, 04.40.+c, 98.10. +z

Singularity Theorems and Their Consequences

“…T he mat ching of f lrw with Vaidya in the general case was succesfully achieved and int erpreted in [73,74] ( see also references therein) . Some applicat ions were lat er developed in [76], upon which this example is based.…”

“…Actually, all cases so far analysed have a good complet e physical int erpretation when carefully st udied, and I am persuaded that the above f lrw+ Vaidya model has an appropriat e int erpretation satisfying the correspondin g ® eld equat ions and boundary condit ions ( see also Refs. 73,74) . T hus, the plausibility of the complete collapse of spherically symmet ric realist ic radiatin g stars wit hout ever forming a singularity or a black-hole region seems feasible.…”

“…Ref. 74) . T he part icular int erpretation is of no import ance for our purp oses as long as the energy-m omentum tensor satis® es the energy condit ions.…”

Black supernovae and black holes in non-local gravity

“…As a consequence, there is no flux of matter through the boundary of the star as well. Therefore, by setting the outer boundary of the cloud at the comoving radius r = r b , which corresponds to the shrinking physical area-radius R b (t) = R(r b , t), we see that we can always perform the matching with an exterior Schwarzschild spacetime with mass parameter M s = F (r b ) [29][30][31][32][33].…”

Compact objects from gravitational collapse: an analytical toy model

“…These include absence of shell-crossing singularities (which implies the condition R > 0), the weak energy condition, which imposes positivity of the energy density (namely ρ > 0) and of the sum of density and pressure (ρ + p > 0), regularity of initial data, and also absence of trapped surfaces at the initial time from which the collapse develops. Finally the collapsing cloud must in general be matched to a generalized Vaidya exterior spacetime at the boundary R b (t) = R(r b , t) in the case where there is a mass inflow or outflow from the star during the collapse phase [22,23]. In the case where the pressure vanishes at the boundary and the Misner-Sharp mass within the boundary is conserved, the matching can be done with an exterior Schwarzschild spacetime [24].…”