Matching of spatially homogeneous nonstationary space-times to vacuum in cylindrical symmetry

Abstract

We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces, singularities and Cauchy horizons. The solutions cannot be asymptotically flat and we present evidence that they are singular on the Cauchy horizons.

Radiative gravitational collapse to spherical, toroidal and higher genus black holes

“…where the interior pressure p and density ρ are defined by the Friedmann equations (2). We note that for b = 1 and Λ = 0, equations (19)- (22) reduce to the ones of [4].…”

Gravitational radiation and the evolution of gravitational collapse in cylindrical symmetry

“…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. It has been shown [20] that, in those cases, the matching hypersurfaces are ruled by geodesics and, from the point of view of the exterior, can be parametrized as…”

“…where H = denotes evaluation at H. In order to solve the matching problem, the strategy followed in [20] was as follows: For a suitable spacetime interior to (31) and for the conditions (35) at the boundary, one obtains an explicit solution for R(ρ, T ) which satisfies the wave equation (77) and the constraints (79) and (80), at H. In turn, the remaining Einstein equations (76) and (78) can be seen as providing γ ,ρρ and ψ ,ρρ on H. Since we know data for the exterior metric and its normal derivatives at the boundary, it then follows [20] that a unique ψ exists on a neighbourhood D of H. Since γ H = ψ and γ ,ρ H = ψ ,ρ , once we have ψ, we use a similar argument in (76) to get a unique γ in D.…”

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

“…For a dust spacetime composed only of fermions, the effective mass-energy density is given by the sum in Eq. (27) and it takes infinite values if, at least, one term of the sum, ρ ieff , is infinite. Although we shall restrain ourselves from imposing any of the usual energy conditions, we shall consider that if any of the parameters that characterize the fluid take complex values at any point of the space-time, the solution is unphysical.…”