On the Penrose Inequality

The purpose of this Letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch’s original proposal for a proof of the positive-energy theorem which was later adapted by Jang and Wald to apply to initial data sets containing apparent horizons. The new input is to dispense with the a priori restriction to an initial data set and to use the four-dimensional structure of spacetime in an essential way.