Back Reaction of 4D Conformal Fields on Static Geometry

Static, spherically symmetric solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the near-horizon geometry, and that the existence of the horizon requires fine-tuning.