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We use the black hole entropy function to study the effect
of Born-Infeld terms on the entropy of spherically symmetric
extremal black holes in heterotic string theory in four
dimensions. We show
that the Born-Infeld terms are capable of stretching the horizon
of a small black hole and the resulting entropy is finite.
We add higher curvature terms of the Gauss-Bonnet type and study
the resulting attractor equations. In the $\alpha' \rightarrow 0$
limit, our results are in conformity with
the ones for standard two charge black holes in heterotic string
theory.
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