Causal configurations of homogeneous energy density in general relativity

Abstract

If the causality condition [the speed of sound always remains less than that of light in vacuum, i. e., $v\le c=1$] is imposed on the spheres of homogeneous energy density, the `ratio of the specific heats', $\gamma \le 2.59457$, constraints the compaction parameter, $u[\equiv (M/a)$, mass to size ratio in geometrized units] of the dynamically stable configurations $\le 0.34056$ [corresponding to a surface redshift $(z_a)\le 0.771$]. 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 $5.4M_{\odot }$, if we substitute the density at the surface of the configuration equal to the average nuclear density, $E=2\times 10^{14}$ g cm${}^{-3}$ [e.g. {\it Nature}, {\bf 259}, 377 (1976)]. (ii) However, if the density of the static configuration is constrained to the value $1.072\times 10^{14}$ g cm${}^{-3}$, 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 $7.4M_{\odot }$. 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 $1.442M_{\odot }$ neutron star to be 0.3041 ms. (iv) A suitable stable model of ultra-compact objects [$u>(1/3)$] which has important astrophysical significance.

7 pages (including 1 figure)

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