Reversing the null limit of the Szekeres metric

Abstract

The null limits of the Lemaitre-Tolman and Szekeres spacetimes are known to be the Vaidya and news-free Robinson-Trautman metrics. We generalise this result to the case of non-zero ?, and then ask whether the reverse process is possible-is there a systematic procedure to retrieve the timelike-dust metric from the null-dust case? We present such an algorithm for re-constructing both the metric and matter tensor components of the timelike-dust manifold.

This undertaking has elucidated the null limit process, highlighted which quantities approach unity or zero, and necessitated a careful discussion of how the functional dependencies are managed by the transformations and substitutions used.

Keywords

• cosmology
• inhomogeneous models
• null limit
• Szekeres metric
• Robinson– Trautman metric
• Vaidya metric
• Kinnersley rocket