On dynamical stability of supermassive objects

Mathematics – Logic

Scientific paper

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Astronomical Models, Dynamic Stability, Quasars, Red Shift, Relativity, Cosmology, Gravitational Effects, Spheres, Stellar Envelopes

Scientific paper

The central redshift of a linear series of massive spheres with an isothermal core and an envelope is calculated within the framework of general relativity. It is noted that Bondi's (1964) static models of massive spheres correspond to a member of the series and that the central redshift is an increasing function of the ratio of the pressure at the center to the pressure at the core-envelope boundary. Two kinds of envelopes are considered: adiabatically stable ones and a thin-mass shell. Stability analysis shows that a massive sphere becomes dynamically unstable as the central redshift is increased and that the critical value of the central redshift is 1.48, 2.82, or 4.43, depending on the core and envelope equations of state. Based on these results, it is concluded that the central redshift cannot exceed 1.5 for the Hoyle-Fowler (1967) model of quasars and that quasar redshifts may be due to both cosmological and gravitational effects.

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