Nonminimal coupling and quantum entropy of a black hole

Formulating the statistical mechanics for a scalar field with nonminimal ξRφ² coupling 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 a statistical entropy dependent on the nonminimal coupling. For ξ<0 the entropy renormalizes the classical Bekenstein-Hawking entropy in the correct way and agrees with the result previously obtained within the conical singularity approach. For a positive ξ, however, the results differ.