Positivity of the Bondi energy

Abstract

We give a new proof that the Bondi momentum is time-like and future directed. This is done by extending a theorem showing the existence of solutions of Witten’s equation on a complete, asymptotically flat surface, to the case where the surface is asyptotically hyperbolic and spans a cut Ŝ of ℐ+. By choosing appropriate boundary conditions the positivity of the Bondi energy is also shown for the case where the surface is no longer free of inner boundaries but is internally bounded by the union of a finite number of marginally trapped surfaces. This argument also applies to the case of asymptotically flat surfaces.