A generalized action for strings which is a sum of the Nambu-Goto and the extrinsic curvature (the energy integral of the surface) terms, is used to couple strings to gravity. It is shown that the conical singularity has deficit angle that has contributions from both the above terms. It is found that the effect of extrinsic curvature is to oppose that of the N-G action for the temperature of the black-hole and to modify the entropy-area relation.
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