Cylindrically symmetric inhomogeneous dust collapse with a zero expansion component

Abstract

We investigate a class of cylindrically symmetric inhomogeneous Λ-dust spacetimes which have a regular axis and some zero expansion component. For Λ = 0, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For Λ = 0, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.

Gravitational radiation and the evolution of gravitational collapse in cylindrical symmetry

“…where α ∈ R \ {0}. As the previous two cases, one can also show that this metric is an interior to Einstein-Rosen type metrics [2] and it is, thus, an interesting case to study by comparison with the spatially homogeneous cases. In this case, the equality of the first fundamental forms on H gives…”

“…Dust matter sources to such spacetimes were studied in [20,2], where the matching between collapsing interior spacetimes and Einstein-Rosen type of exteriors was shown to exist along timelike hypersurfaces. It would be therefore interesting to study the gravitational radiation through those hypersurfaces and to find out whether it enhances the gravitational collapse or not.…”

“…On the right panel, a cut of the spacetime is depicted for r < α/ √ 2. This figure is adapted from [2].…”

Influence of intrinsic spin in the formation of singularities for inhomogeneous effective dust space-times

“…where γ ∈ R\ {0}, β ∈ R ≥0 , r > 0, z ∈ ]−∞, +∞[ and ϕ ∈ [0, 2π[. A space-time exterior to (55) was found in [26]. Assuming that the space-time is permeated by effective dust, we find that the effective mass-energy density is given by…”

“…When considering the case of the gravitational collapse of a compact object in astrophysics, we consider a model of Oppenheimer-Snyder type having a collapsing interior given by the Szekeres metric [24,25], which is inhomogeneous, matched to a vacuum exterior. Examples of such models were shown to exist in [26][27][28]. Whereas, when considering a cosmological model, we shall assume that the coordinates in the Szekeres metric are globally defined and that the universe can either initially be expanding or contracting.…”