Relativistic supermassive stars

A plausible scenario for the formation of a stable supermassive star in the relativistic regime has been discussed. The onset of the negativity of the 'distribution function' in the stable sequences of the star clusters [the stability of star clusters is assured by using the variational method (Chan drasekhar, 1964a,b) for equivalent gas spheres] described by Tolman's type VII solution with vanishing surface density has been regarded as an indicat ion of the conversion of the cluster structure into a supermassive star. Fo r the critical values of the 'adiabatic index', (4/3) < gamma (crit) less t han or equal to (5/3) (for which a supermassive star represent neutrally st able system), the mass, and the size of this object comes out to be 6.87 x 10(7) M-. less than or equal to M less than or equal to 1.7 x 10(9)M(.), an d 2.74x 10(14) cm less than or equal to a less than or equal to 1.43 x 10(1 5) cm respectively, for the central temperature, T-0 = 6x 10(7) degreesK, w hich is sufficient for the release of nuclear energy. The total energy rele ased during their evolution ranges from 2.46 x 10(60) - 3.18 x 10(62) erg, which is sufficient to power these objects at least for a period of similar to 10(6) - 10(7) years. These figures agrees quite well with those cited f or Quasi Stellar Objects (QSOs) in the literature.