Abstract
The classical Penrose inequality relates the mass of an asymptotically flat spacetime to the total area of its black holes. We present a PDE-based proof of the Penrose inequality for a special class of perturbations of Schwarzschild initial data. The proof is based around linearising solutions to a version of the Jang equation which is modified to deal with warped product metrics. We discuss the possibility of generalising the argument to a wider class of perturbations.
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