Constant mean curvature slices and trapped surfaces in asymptotically flat spherical spacetimes.

Abstract

We investigate trapped surfaces in asymptotically flat spherical spacetimes using constant mean curvature slicing. Precise necessary and sufficient conditions for the formation of such surfaces are derived. We write down an explicit expression for the constant mean curvature foliation of the Reissner-Nordstr\"om spacetime. A set of criteria describing the formation of horizons in arbitrary slicings of asymptotically flat and spherically symmetric spacetimes is given in the Appendix.