Quantum gravitational correction to the Hawking temperature from the Lemaître-Tolman-Bondi model

We solve the quantum constraint equations of the Lemaître-Tolman-Bondi model in a semiclassical approximation in which an expansion is performed with respect to the Planck length. We recover in this way the standard expression for the Hawking temperature as well as its first quantum gravitational correction. We then interpret this correction in terms of the one-loop trace anomaly of the energy-momentum tensor and thereby make contact with earlier work on quantum black holes.