Stretching the horizon of a higher dimensional small black hole

There is a general scaling argument that shows that the entropy of a smallblack hole, representing a half-BPS excitation of an elementary heteroticstring in any dimension, agrees with the statistical entropy up to an overallnumerical factor. We propose that for suitable choice of field variables thenear horizon geometry of the black hole in D space-time dimensions takes theform of AdS_2\times S^{D-2} and demonstrate how this ansatz can be used tocalculate the numerical factor in the expression for the black hole entropy ifwe know the higher derivative corrections to the action. We illustrate this bycomputing the entropy of these black holes in a theory where we modify thesupergravity action by adding the Gauss-Bonnet term. The black hole entropycomputed this way is finite and has the right dependence on the charges inaccordance with the general scaling argument, but the overall numerical factordoes not agree with that computed from the statistical entropy except for D=4and D=5. This is not surprising in view of the fact that we do not use a fullysupersymmetric action in our analysis; however this analysis demonstrates thathigher derivative corrections are capable of stretching the horizon of a smallblack hole in arbitrary dimensions.Comment: LaTeX file, 26 pages; v2: a simple expression for entropy is given and references adde