We solve the dilaton field equation in the background of a spherically symmetric black hole in bosonic or heterotic string theory with curvature-squared corrections in arbitrary d spacetime dimensions. We then apply this result to obtain a spherically symmetric black hole solution with dilatonic charge and curvature-squared corrections in bosonic or heterotic string theory compactified on a torus. For this black hole, we obtain its free energy, entropy, temperature, specific heat, and mass.
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Filipe Moura (2011) studied this question.
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