IMPLODING SCALAR FIELDS

Static spherically symmetric uncoupled scalar space-times have no even t horizon and a divergent Kretschmann singularity at the origin of the coordinates. The singularity is always present so that nonstatic solu tions have been sought to see if the singularities can develop from an initially singular free space-time. In flat space-time the Klein-Gord on equation rectangle phi = 0 has the nonstatic spherically symmetric solution phi = sigma(v)/r, where sigma(v) is a once differentiable fun ction of the null coordinate v. In particular, the function sigma(v) c an be taken to be initially zero and then grow, thus producing a singu larity in the scalar field. A similar situation occurs when the scalar field is coupled to gravity via Einstein's equations; the solution al so 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 develo ps 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 w ith positive overall energy. This paper presents this solution and sev eral other nonstatic scalar solutions. The properties of these solutio ns which are studied are limited to the following three: (i) whether t he solution can be joined to Minkowski space-time, (ii) whether the so lution is asymptotically flat, (iii) and, if so, what the solutions' B ondi and ADM masses are. (C) 1996 American Institute of Physics.