If the causality condition [ the speed of sound always remains less than that of light in vacuum , i. e. , v \leq c = 1 ] is imposed on the spheres of homogeneous energy density , the ‘ ratio of the specific heats ’ , \gamma \leq 2.59457 , constraints the compaction parameter , u [ \equiv ( M / a ) , mass to size ratio in geometrized units ] of the dynamically stable configurations \leq 0.34056 
[ corresponding to a surface redshift ( z _ { a } ) \leq 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 5.4 M _ { \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 . Nature , 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 7.4 M _ { \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 1.442 M _ { \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 .