NONMINIMAL COUPLING, BOUNDARY TERMS AND RENORMALIZATION OF THE EINSTEIN-HILBERT ACTION AND BLACK-HOLE ENTROPY

According to Gibbons and Hawking a consistent variational procedure ap plied to the gravitational action requires a certain balance between t he volume and boundary parts of the action. We consider the problem of preserving this balance in the quantum effective action for the matte r non-minimally coupled to metric. It is shown that one has to add a s pecial boundary term to the matter action analogous to the Gibbons-Haw king one. This boundary term modifies the one-loop quantum corrections to give a correct balance for the effective action as well. This mean s that the boundary UV divergences do not require independent renormal ization and are automatically renormalized simultaneously with their v olume part. This result is derived for arbitrary non-minimally coupled matter. The example of the 2D Maxwell field is considered in much det ail. The relevance of the results obtained to the problem of the renor malization of the black hole entropy is discussed.