Active Mass Under Pressure

2005/05/10 by Jürgen Ehlers, Juergen Ehlers, Istvan Ozsvath +3 · 2 voices
Earth and Planetary Sciences · Physics and Astronomy · #High-pressure geophysics and materials #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #gr-qc

paper · pdf · doi:10.1119/1.2198881

published as Am.J.Phys. 74 (2006) 607-613 · 28 pages, 4 figures

arxiv created 2005/05/10 · openalex publication_date 2006/07/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.

Discussions

• OP's metric is an example of ultrastatic spacetime, i.e. it is a direct product of a Riemannian manifold (“space”) and $\mathbb R$ (“time”) and thus $-g_{tt}$ can be set to unity everywhere. This mean [stackexchange, 5 points]
• The answers given so far make many good points. One problem with the question is that it's implicitly simplifying the context. So I'd like to give a more detailed answer, which is a qualified "yes". C [stackexchange, 3 points]

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