Imploding scalar fields

Static spherically symmetric uncoupled scalar space-times have no event horizon and a divergent Kretschmann singularity at the origin of the coordinates. The singularity is always present so that nonstatic solutions have been sought to see if the singularities can develop from an initially singular free space-time. In flat space-time the Klein-Gordon equation rectangle phi = 0 has the nonstatic spherically symmetric solution phi = sigma(v)/r, where sigma(v) is a once differentiable function of the null coordinate v. In particular, the function sigma(v) can be taken to be initially zero and then grow, thus producing a singularity in the scalar field. A similar situation occurs when the scalar field is coupled to gravity via Einstein's equations; the solution also develops a divergent Kretschmann invariant singularity, but it has no overall energy. To overcome this, Bekenstein's theorems are applied to give two corresponding conformally coupled solutions. One of these has positive ADM mass and has the following properties: (i) it develops a Kretschmann invariant singularity, (ii) it has no event horizon, (iii) it has a well-defined source, (iv) it has well-defined junction condition to Minkowski space-time, and (v) it is asymptotically flat with positive overall energy. This paper presents this solution and several other nonstatic scalar solutions. The properties of these solutions which are studied are limited to the following three: (i) whether the solution can be joined to Minkowski space-time, (ii) whether the solution is asymptotically flat, (iii) and, if so, what the solutions' Bondi and ADM masses are. (C) 1996 American Institute of Physics.