The patchwork divergence theorem

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/cj82k793z

Descriptions

Attribute Name	Values
Creator	Dray, Tevian Hellaby, Charles
Abstract	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. Keywords:Smooth Manifolds, Differential Geometry, Einstein Field Equations, General Relativity Theory, Metrics, Vector Fields
Resource Type	Article
DOI	https://doi.org/10.1063/1.530719
Date Available	2013-08-20T17:46:22+00:00
Date Issued	1994-11
Citation	Dray, T., & Hellaby, C. (1994, November). The patchwork divergence theorem. Journal of Mathematical Physics, 35(11), 5922-5929. doi:10.1063/1.530719
Journal Title	Journal of Mathematical Physics
Journal Volume	35
Journal Issue/Number	11
Academic Affiliation	Mathematics
Rights Statement	Copyright Not Evaluated
Funding Statement (additional comments about funding)	T.D. was partially funded by NSF Grant No. PHY-9208494. C.H. would like to thank the FRD for a research grant.
Publisher	American Institute of Physics
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/41857