On the Penrose inequality

Abstract

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.

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