Causal Configurations of Homogeneous Energy Density in General Relativity

If the causality condition [the speed of sound always remains less than that of light in vacuum, i. e., v ≤ c = 1] is imposed on the spheres of homogeneous energy density, the ‘ratio of the specific heats’, γ ≤ 2.59457, constraints the compaction parameter, u[≡ (M/a), mass to size ratio in geometrized units] of the dynamically stable configurations ≤ 0.34056 [corresponding to a surface redshift (za) ≤ 0.771]. Apparently, The maximum value of u obtained in this manner belongs to an absolute upper bound, and gives: (i) The maximum value for static neutron star masses as 5.4M⊙, if we substitute the density at the surface of the configuration equal to the average nuclear density, E = 2×10 g cm [e.g. Nature, 259, 377 (1976)]. (ii) However, if the density of the static configuration is constrained to the value 1.072 × 10 g cm, by imposing the empirical result that the minimum rotation period of the fastest rotating pulsar known to date, PSR 1937 + 21, is 1.558 ms, the maximum mass value for static neutron stars exceed upto 7.4M⊙. These masses have important implications for the massive compact objects like Cyg X-1, Cyg XR-1, and LMC-X3 etc., which may not, necessarily, represent black holes. (iii) The minimum rotation periods for a static 1.442M⊙ neutron star to be 0.3041 ms. (iv) A suitable stable model of ultra-compact objects [u > (1/3)] which has important astrophysical significance.