  We analyze the 3-parameter family of exact, regular, static, spherically
symmetric perfect fluid solutions of Einstein's equations (corresponding to a
2-parameter family of equations of state) due to Pant and Sah and
"rediscovered" by Rosquist and the present author. Except for the Buchdahl
solutions which are contained as a limiting case, the fluids have finite radius
and are physically realistic for suitable parameter ranges. The equations of
state can be characterized geometrically by the property that the 3-metric on
the static slices, rescaled conformally with the fourth power of any linear
function of the norm of the static Killing vector, has constant scalar
curvature. This local property does not require spherical symmetry; in fact it
simplifies the the proof of spherical symmetry of asymptotically flat solutions
which we recall here for the Pant-Sah equations of state. We also consider a
model in Newtonian theory with analogous geometric and physical properties,
together with a proof of spherical symmetry of the asymptotically flat
solutions.
