Does the Principle of Equivalence Prohibit Trapped Surfaces from Forming in the General Relativistic Collapse Process

Abstract

It has recently been shown that time-like spherical collapse of a physical fluid in General Relativity does not permit formation of “trapped surfaces.” This result followed from the fact that the formation of a trapped surface in a physical fluid would cause the time-like world lines of the collapsing fluid to become null at the would-be trapped surface, thus violating the Principle of Equivalence in General Theory of Relativity (GTR). For the case of the spherical collapse of a physical fluid, the “no trapped surface condition” 2GM(r, t)/R(r, t) c2 0, where zs is the surface red shift seen by a zero-angular momentum observer. When this condition is applied to the first integral of the time-time component of the Einstein equation, it leads to the “no trapped surface condition” 2GM(rs, t)/R(rs, t) c2<1 consistent with the condition obtained above for the interior co-moving metric. The Principle of Equivalence enforces the “no trapped surface condition” by constraining the physics of the general relativistic radiation transfer process in a manner that requires it to establish and maintain an Eddington limited secular equilibrium on the dynamics of the collapsing radiating surface so as to always keep the physical surface of the collapsing object outside of its Schwarzschild radius. The important physical implication of the “no trapped surface condition” is that galactic black hole candidates GBHC do not possess event horizons and hence do possess intrinsic magnetic fields. In this context the spectral characteristics of galactic black hole candidates offer strong evidence that their central nuclei are highly red-shifted Magnetospheric Eternally Collapsing Objects (MECO) within the framework of General Relativity.