PERTURBATION OF INITIAL DATA FOR SPHERICALLY SYMMETRICAL CHARGED BLACK-HOLE AND PENROSE CONJECTURE

A new description of unconstrained degrees of freedom for the gravitational field introduced in [6] has been applied to the description of perturbed initial data from the Reissner-Nordstrom solution. When this solution describes a black hole (m > q) we can perform a generic fully nonlinear perturbation of initial data outside an apparent horizon in such a way that this horizon is an extremal two-surface in four-dimensional spacetime. A simple consequence of the considerations in: J. Jezierski, Classical Quantum Gravity 11, 1055 (1994) leads to the following theorem: Let SIGMA be an asymptotically flat spacelike surface which is nonsingular outside an extremal two-surface S(min) (which is extremal as two-surface imbedded in spacetime) then 16pim2ADM greater-than-or-equal-to A, where m(ADM) denotes the A.D.M. mass of perturbed data (around Reissner-Nordstrom solution) on SIGMA and A is an area of the apparent horizon S(min).