Matching LTB and FRW space-times through a null hypersurface

S. Khakshournia1 and R. Mansouri2

Abstract

Matching of a LTB metric representing dust matter to a background FRW universe across a null hypersurface is studied. In general, 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 vanishing pressure or energy density on the hypersurface are 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 configuration can only be joined smoothly to a flat LTB one.

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