  There is a general scaling argument that shows that the entropy of a small
black hole, representing a half-BPS excitation of an elementary heterotic
string in any dimension, agrees with the statistical entropy up to an overall
numerical factor. We propose that for suitable choice of field variables the
near horizon geometry of the black hole in D space-time dimensions takes the
form of AdS_2\times S^{D-2} and demonstrate how this ansatz can be used to
calculate the numerical factor in the expression for the black hole entropy if
we know the higher derivative corrections to the action. We illustrate this by
computing the entropy of these black holes in a theory where we modify the
supergravity action by adding the Gauss-Bonnet term. The black hole entropy
computed this way is finite and has the right dependence on the charges in
accordance with the general scaling argument, but the overall numerical factor
does not agree with that computed from the statistical entropy except for D=4
and D=5. This is not surprising in view of the fact that we do not use a fully
supersymmetric action in our analysis; however this analysis demonstrates that
higher derivative corrections are capable of stretching the horizon of a small
black hole in arbitrary dimensions.
