The statistical-mechanical origin of the Bekenstein-Hawking entropy S BH in the induced gravity is discussed. In the framework of the induced gravity models the Einstein action arises as the low energy limit of the effective action of quantum fields. The induced gravitational constant is determined by the masses of the heavy constituents. We established the explicit relation between statistical entropy of constituent fields and black hole entropy S BH .
We determine the s-waves contribution of a scalar field to the four dimensional effective action for arbitrary spherically symmetric external gravitational fields. The result is applied to 4d-black holes and it is shown that the energy momentum tensor derived from the (nonlocal) effective action contains the Hawking radiation. The luminosity is close to the expected one in the s-channel. The energy momentum tensor may be used as starting point to study the backreaction problem.
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