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We explore use of the harmonic Einstein equations to numerically find stationary black holes where the problem is posed on an ingoing slice that extends into the interior of the black hole.
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It is interesting to contrast this with the solutions of Dias et al. 2011 which have a Killing horizon, but are neither stationary nor axisymmetric if one considers the metric and matter. However, considering the metric alone, the solution is stationary and does rigidly rotate. We refer to rigidity with reference to the metric alone in this work
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