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A classical model for the extension of singular spacetime geometries acrosstheir singularities is presented. The regularization introduced by this modelis based on the following observation. Among the geometries that satisfyEinstein's field equations there is a class of geometries, with certainsingularities, where the components of the metric density and their partialderivatives remain finite in the limit where the singularity is approached.Here we exploit this regular behavior of the metric density and elevate itsstatus to that of a fundamental variable -- from which the metric isconstructed. We express Einstein's field equations as a set of equations forthe metric density, and postulate junction conditions that the metric densitysatisfies at singularities. Using this model we extend certain geometriesacross their singularities. The following examples are discussed: radiationdominated Friedmann-Robertson-Walker Universe, Schwarzschild black hole,Reissner-Nordstr\"{o}m black hole, and certain Kasner solutions. For all of theabove mentioned examples we obtain a unique extension of the geometry beyondthe singularity.

Junction conditions at spacetime singularities