Yes, black holes exist in gravitational theories with unbounded speeds of propagation

Gravitational theories with broken Lorentz invariance have attracted a great deal of interest as they provide a test-bed of LI and offer a mechanism to improve their ultraviolet behavior, so that the theories may be renormalizable. However in such theories, particles can travel with arbitrary velocities and black holes may not exist at all. In contrast to this expectation, it has been shown that an absolute horizon exists, which traps signals despite infinitely large velocities.

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