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Petrov type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math> equation on horizons of nontrivial bundle topology
We consider three-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context, we consider the Petrov type $D$ equation introduced and studied in previous works [D. Dobkowski-Ry\l{}ko, J. Lewandowski, and T. …