The Penrose inequality for perturbations of the Schwarzschild initial data

@article{Kopiski2019ThePI,
  title={The Penrose inequality for perturbations of the Schwarzschild initial data},
  author={J Kopiński and J Tafel},
  journal={Classical and Quantum Gravity},
  year={2019},
  volume={37}
}
We show that in the conformally flat case the Penrose inequality is satisfied for the Schwarzschild initial data with a small addition of the axially symmetric traceless exterior curvature. In this class the inequality is saturated only for data related to special sections of the Schwarzschild spacetime. 
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