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A lower bound for the mass of axisymmetric connected black hole data sets
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datamassaxisymmetricblackconnectedholesetsbound
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We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric.
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