Reflections on the Energy of Black Holes

Abstract

Inside a black hole, there is no local way to say which side of a sphere is the inside, and which is the outside. One can easily be gulled by this fact into mixing up the sign of the energy. We lead the reader astray with a na\"ive treatment of the energy of a null shell in black hole spacetimes. We then resolve the confusion, showing that global, rather than local, considerations offer good guidance.