Pandora's box lid: geometry near the apparent horizon

Formation of a trapped region with a singularity-free apparent horizon in finite time of a distant observer has important physical consequences. In spherical symmetry it implies that only two classes of solutions of the Einstein equations are possible. In both cases the null energy condition (NEC) is violated and an expanding trapped region leads to a firewall. The weighted time average of the energy density for an observer crossing this firewall is negative and exceeds the maximal NEC violation that quantum fields can produce. For a contracting trapped region both metrics approach the ingoing Vaidya metric with decreasing mass. None ofthe solutions leads to a static limit. Only one class of solutions allows for a test particle to cross the apparent horizon, and produces a black hole at the end of a thin shell collapse. These results significantly constrain the regular black hole models.