Physics
Scientific paper
Nov 1964
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1964rspsa.282..303b&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 282, Issue 1390, pp. 303-317
Physics
111
Scientific paper
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 = 1/2 cannot be attained except perhaps under conditions of severe tension. It is shown that if u is everywhere less than 1/2, 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 ldots, while if in addition the density is nowhere less than three times the pressure and nowhere increasing outwards, then u <=slant 0.319.
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