Vacuum spherically symmetric Einstein gravity in (N≥4) dimensions can be cast in a two-dimensional conformal nonlinear sigma model form by first integrating on the (N - 2)-dimensional (hyper)sphere and then performing a canonical transformation. The conformal sigma model is described by two fields which are related to the Arnowitt-Deser-Misner (ADM) mass and to the radius of the (N - 2)-dimensional (hyper)sphere, respectively. By quantizing perturbatively the theory we estimate the quantum corrections to the ADM mass of a black hole.
M. Cavaglia and C. Ungarelli, "Quantum Gravity Corrections to the Schwarzschild Mass," Physical Review D - Particles, Fields, Gravitation and Cosmology, vol. 61, no. 6, American Physical Society (APS), Feb 2000.
The definitive version is available at https://doi.org/10.1103/PhysRevD.61.064019
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