We present a new solution in Einstein's general relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst equations for stationary and axisymmetric spacetimes. This kind of Ehlers transformation is able to embed any given solution into a rotating background, which is not of Newman-Unti-Tamburino type. We analyze the physical properties, ergoregions and geodesics of the new metric, which is regular outside the event horizon and has a well-defined thermodynamics. We finally consider the Kerr generalization.
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Astorino et al. (2022) studied this question.
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