Semiclassical rotating AdS black holes with quantum hair in holography

In the context of AdS/CFT duality, we study semiclassical stationary rotating AdS black holes with nontrivial quantum hair in three and five dimensions. We construct these solutions by perturbing the Bañados-Teitelboim-Zanelli (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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo>∼</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:msup><a:mi>λ</a:mi><a:mi>n</a:mi></a:msup></a:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>n</c:mi><c:mo>=</c:mo><c:mn>1</c:mn></c:mrow></c:math>, 2) along a radial null geodesic as the affine parameter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>λ</e:mi></e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>C</g:mi><g:mn>0</g:mn></g:msup></g:math>-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.