The Patchwork Divergence Theorem
广义相对论与量子宇宙学
2011-07-19 v1 dg-ga
微分几何
摘要
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PACS numbers 4.20.Cv, 04.20.Me, 11.30.-j, 02.40.Hw)
引用
@article{arxiv.gr-qc/9404002,
title = {The Patchwork Divergence Theorem},
author = {Tevian Dray and Charles Hellaby},
journal= {arXiv preprint arXiv:gr-qc/9404002},
year = {2011}
}
备注
REVTeX 3.0, 7 pages by default (16 in preprint style), no figures