Reversing the Null Limit of the Szekeres Metric
arXiv:2007.11350 · doi:10.1088/1361-6382/abcc0c
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.
LaTeX, 17pp, no figures, includes referee and proofreader amendments, to appear in CQG