  We study a holographic construction of quantum rotating BTZ black holes that
incorporates the exact backreaction from strongly coupled quantum conformal
fields. It is based on an exact four-dimensional solution for a black hole
localized on a brane in AdS$_4$, first discussed some years ago but never fully
investigated in this manner. Besides quantum CFT effects and their
backreaction, we also investigate the role of higher-curvature corrections in
the effective three-dimensional theory. We obtain the quantum-corrected
geometry and the renormalized stress tensor. We show that the quantum black
hole entropy, which includes the entanglement of the fields outside the
horizon, satisfies the first law of thermodynamics exactly, even in the
presence of backreaction and with higher-curvature corrections, while the
Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather
non-trivial bulk calculation, shows the consistency of the holographic
interpretation of braneworlds. We compare our renormalized stress tensor to
results derived for free conformal fields, and for a previous holographic
construction without backreaction effects, which is shown to be a limit of the
solutions in this article.
