Semiclassical Rotating AdS Black Holes with Quantum Hair in Holography

In the context of the AdS/CFT duality, we study semiclassical stationary rotating AdS black holes with non-trivial quantum hair in three and five dimensions. We construct these solutions by perturbing the BTZ black hole and the five-dimensional Myers-Perry AdS black hole according to holographic semiclassical equations. In the three-dimensional case, the vacuum expectation value of the stress-energy tensor diverges as $\sim 1/\lambda^n~(n=1,2)$ along a radial null geodesic as the affine parameter $\lambda$ approaches zero at the Cauchy horizon, depending on the type of perturbation. In the five-dimensional case, most hairy solutions exhibit strong divergences, either in the stress-energy tensor or in the parallelly propagated Riemann components, along the radial null geodesic crossing the Cauchy horizon. Nevertheless, there exists a specific class of semiclassical solutions that retain a $C^0$-regular Cauchy horizon, where perturbations remain bounded. For extremal black holes, the vacuum expectation value of the stress-energy tensor diverges along a radial null geodesic transverse to the event horizon in both three and five dimensions, even though all components of the perturbed metric vanish in this limit.