Radiation pressure supported stars in Einstein gravity: eternally collapsing objects

Abstract

Even when we consider Newtonian stars, that is, 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. We point out that this requirement for excessively large M in the Newtonian case is a consequence of the occurrence of low z≪ 1. However, if we remove such restrictions, and allow for the possible occurrence of a highly general relativistic regime, z≫ 1, we show that it is possible to have radiation pressure supported stars (RPSSs) at an arbitrary value of M. Since RPSSs 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 (BH) stage characterized by z=∞. Thus, late stages of BH formation, by definition, would have z≫ 1, and hence would be examples of quasi-stable general relativistic RPSSs. It is shown that the observed duration of such Eddington limited radiation pressure dominated states is t≈ 5 × 108 (1 +z) yr. Thus, t→∞ as BH formation (z→∞) takes place. Consequently, such radiation pressure dominated extreme general relativistic stars become eternally collapsing objects (ECOs) 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 and the value of the integration constant in the vacuum Schwarzschild solution is zero. Hence the supposed observed BHs are actually ECOs.