Radiation pressure supported stars in Einstein gravity: eternally collapsing objects

Even when we consider Newtonian stars, i.e., stars with surface gravitational redshift, z ≪ 1, it is well known that, theoretically, it is possible to have stars, supported against self-gravity, almost entirely by radiation pressure. However, such Newtonian stars must necessarily be supermassive(HoyFow 1963; Fowler 1966; Weinberg 1972). We point out that this requirement for excessive large M in Newtonian case, is a consequence of the occurrence of low z ≪ 1. But if we remove such restrictions, and allow for possible occurrence of highly general relativistic regime, z ≫ 1, we show that, it is possible to have radiation pressure supported stars at arbitrary value of M. Since radiation pressure supported stars necessarily radiate at the Eddington limit, in Einstein gravity, they are never in strict hydrodynamical equilibrium. Further, it is believed that sufficiently massive or dense objects undergo continued gravitational collapse to the Black Hole stage characterized by z = ∞. Thus, late stages of Black Hole formation, by definition, will have, z ≫ 1, and hence would be examples of quasistable general relativistic radiation pressure supported stars (Mitra 2006). It is shown that the observed duration of such Eddington limited radiation pressure dominates states is t ≈ 5 × 10 8 (1 + z) yr. Thus, t → ∞ as Black Hole formation (z → ∞) would take place. Consequently, such radiation pressure dominated extreme general relativistic stars become Eternally Collapsing Objects (ECOs) and and the BH state is preceded by such an ECO phase. This result is also supported by our previous finding that trapped surfaces are not formed in gravitational collapse(Mitra1 2005) and the value of the integration constant in the vacuum Schwarzschild solution is zero(Mitra2