On the Penrose inequality for general horizons.

@article{Malec2002OnTP,
  title={On the Penrose inequality for general horizons.},
  author={Edward J Malec and Marc Mars and Walter Simon},
  journal={Physical review letters},
  year={2002},
  volume={88 12},
  pages={
          121102
        }
}
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons… 
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References

SHOWING 1-10 OF 33 REFERENCES
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Phys
  • Rev. D 49, 6467
  • 1994
Phys
  • Rev. Lett. 87, 101101-1
  • 2001
Geom
  • Geom
J. Math. Phys. J. Math. Phys
  • J. Math. Phys. J. Math. Phys
  • 1978
Commun
  • Math. Phys. 88, 295
  • 1983
Ann. N.Y. Acad. Sci
  • Ann. N.Y. Acad. Sci
  • 1973
J. Math. Phys. (N.Y.)
  • J. Math. Phys. (N.Y.)
  • 1968
Phys. Rev. D
  • Phys. Rev. D
  • 1994
...
...