Stretching the Horizon of a Higher Dimensional Small Black Hole

TL;DR

This paper explores how higher derivative corrections affect the horizon geometry and entropy of small black holes in higher dimensions, showing that these corrections can extend the horizon but do not always match statistical entropy calculations.

Contribution

It demonstrates that higher derivative terms can modify the horizon of small black holes in arbitrary dimensions, providing a method to compute entropy corrections beyond supergravity.

Findings

Entropy matches statistical predictions in D=4 and D=5.

Higher derivative corrections can stretch the horizon in arbitrary dimensions.

Numerical factors differ from statistical entropy outside D=4 and D=5.

Abstract

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.