Title: "Active mass under pressure"
After a historical introduction to Poisson's equation in Newtonian gravity I
review its analog for static gravitational fields in Einstein's theory.
Here, the source of the potential, that might be called the active mass
density, on the right-hand side of the equation, comprises not only all
possible sources of energy but in addition to that the term 3p/c^2. In the
Hamburg seminar on relativity in the fifties we discussed whether the 3p/c^2
term due to Fermi pressure in different atomic nuclei could be detected in
Cavendish type experiments. This question is connected with the Tolman
paradox. Our reasoning at that time did contain an instructive mistake that
we were able to resolve now. We conclude that the 3p/c^2 term should not
lead to discrepancies for different materials in a Cavendish type experiment
although of importance in the early universe and collapsing stellar cores.
A paper with this title will appear in the June 2006 issue of The American
Journal of Physics.
A further discussion of the problem using exact solutions has been published
by J. Ehlers et al.
"Pressure as a Source of Gravity", Physical Review D, vol. 72, 124003
(2005). This paper will also be reviewed.