Gravitational decoupling, hairy black holes and conformal anomalies

Hairy black holes in the gravitational decoupling setup are studied from the perspective of conformal anomalies. Fluctuations of decoupled sources can be computed by measuring the way the trace anomaly-to-holographic Weyl anomaly ratio differs from the unit. Therefore the gravitational decoupling parameter governing three hairy black hole metrics is then bounded to a range wherein one can reliably emulate AdS/CFT with gravitational decoupled solutions, in the tensor vacuum regime.