On the continuation of orthogonal structure across a surface of discontinuity in the momentum-energy tensor.

by Dominic G. B. Edelen

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback11 pages $15.00 $12.00 20% Web Discount

A discussion of Einstein's general relativity field equations, the study of which is usually begun by assuming certain particular forms for the metric tensor. In the presence of a general momentum-energy tensor that admits jump discontinuities, the question arises as to the consistency of the assumed metric structure in regions where the jumps in the momentum-energy tensor occur. To answer this question, the author examines the continuation of orthogonal structure across surfaces of discontinuity in the momentum-energy tensor and analyzes the problems of several massive bodies of finite extent. It is concluded that, although orthogonal structure for problems of the second and third classes can generally be continued, the problems of the first class will only admit orthogonal structure, everywhere in the space under very particular circumstances.

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.