Abstract
The exact relativistic form of the equation of hydrostatic support by an isotropic pressure is found in an especially convenient form. A quantity
u
, the natural generalization of Schwarzschild’s
m/r
ratio at the surface, is used, and it is proved that the critical value
u
= ½ cannot be attained except perhaps under conditions of severe tension. It is shown that if
u
is everywhere less than different physical restrictions are significant in well-defined inner and outer zones as far as the attainment of high
u
values is concerned. A number of limiting configurations are derived for physically significant restrictions. In particular it is shown that if the density is nowhere negative then
u
< 0.485 ..., while if in addition the density is nowhere less than three times the pressure and nowhere increasing outwards, then
u
< 0.319.
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