Feasibility of singularity avoidance for a collapsing object due to a scalar field

Abstract

We study the problem of the gravitational collapse of an object as seen by an external observer. We assume that the resultant spacetime is a match of an external Vaidya spacetime with an interior Friedmann-Lemaître-Robertson-Walker (FRLW) spacetime of any spatial curvature and with a scalar field both minimally and non-minimally coupled to the metric. With the goal of studying a contracting (collapsing) object, for the initial moment of observation we take that its energy density and pressure are positive, that there are no trapping surfaces, and that the null energy condition (NEC) and the strong energy condition (SEC) are fulfilled. We show that there are many cases where singularities could be avoided for both the minimal and non-minimal couplings, although the contexts for so are very different in both cases. For the minimal coupling, the avoidance of singularities could happen either through evaporation or altogether, triggered by a violation of the SEC for a period of time. For the non-minimal coupling, the complete singularity avoidance happens only if evaporation takes place, and a temporary violation of the SEC does not thwart the formation of singularities. The above results show the relevance of the global (the whole spacetime) validity of energy conditions for the singularity theorems to be applicable; otherwise, the fate of a collapsing star is not known a priori. At the same time, the surface behavior of a collapsing body offers partial diagnostics of what happens in the inaccessible regions of spacetime to external observers. Our analyses suggest that a bounce behavior of the surface of the initially collapsing object is a fingerprint of the SEC violation in its interior, and that could be due to the existence of scalar fields there.