Matching LTB and FRW spacetimes through a null hypersurface

TL;DR

This paper investigates the conditions under which LTB dust spacetimes can be matched to FRW universes across null hypersurfaces, revealing constraints on curvature and the nature of the boundary.

Contribution

It provides a detailed analysis of null hypersurface matching between LTB and FRW spacetimes, including special cases with vanishing pressure or energy density.

Findings

Matching is only possible if the FRW background is flat or open.

No gravitational impulsive wave is generally present on the null hypersurface.

A flat FRW can only be smoothly joined to a flat LTB.

Abstract

Matching of a LTB metric representing dust matter to a background FRW universe across a null hypersurface is studied. In general, an unrestricted matching is possible only if the background FRW is flat or open. There is in general no gravitational impulsive wave present on the null hypersurface which is shear-free and expanding. Special cases of the vanishing pressure or energy density on the hypersurface is discussed. In the case of vanishing energy momentum tensor of the null hypersurface, i.e. in the case of a null boundary, it turns out that all possible definitions of the Hubble parameter on the null hypersurface, being those of LTB or that of FRW, are equivalent, and that a flat FRW can only be joined smoothly to a flat LTB.