Positive mass theorems for black holes

  title={Positive mass theorems for black holes},
  author={G. Gibbons and S. Hawking and G. Horowitz and M. Perry},
  journal={Communications in Mathematical Physics},
We extend Witten's proof of the positive mass theorem at spacelike infinity to show that the mass is positive for initial data on an asymptotically flat spatial hypersurface Σ which is regular outside an apparent horizonH. In addition, we prove that if a black hole has electromagnetic charge, then the mass is greater than the modulus of the charge. These results are also valid for the Bondi mass at null infinity. Finally, in the case of the Einstein equation with a negative cosmological… Expand
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