Active Mass under Pressure

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. 1 Historical Introduction By “active” mass one means the mass considered as source of a gravitational field. This concept can be distinguished from that of the “passive” mass measuring the response to a gravitational field and of an “inertial” mass describing resistance against acceleration by any force, gravitational or other. These distinctions are useful for considering nonNewtonian or non-Einsteinian theories of gravity, or to assess which aspects of mass are