Non-minimal coupling and quantum entropy of black hole

Formulating the statistical mechanics for a non-minimal scalar field in a black hole background we propose modification of the original ’t Hooft “brick wall” prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and allows one to obtain the correct dependence of the statistical entropy on the non-minimal coupling. The entropy renormalizes the classical Bekenstein-Hawking entropy in the correct way and agrees with the result previously obtained within the conical singularity approach. We apply this calculation to a model of induced gravity and demonstrate that the Bekenstein-Hawking entropy can be entirely induced as statistical entropy of constituent fields. PACS number(s): 04.70.Dy, 04.62.+v e-mail: [email protected] 1