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We calculate near-horizon solutions for four-dimensional 4-charge andfive-dimensional 3-charge black holes in heterotic string theory from the partof the ten-dimensional tree-level effective action which is connected togravitational Chern-Simons term by supersymmetry. We obtain that the entropiesof large black holes exactly match the alpha'-exact statistical entropiesobtained from microstate counting (D=4) and AdS/CFT correspondence (D=5).Especially interesting is that we obtain agreement for both BPS and non-BPSblack holes, contrary to the case of R^2-truncated (four-derivative) actions(D-dimensional N=2 off-shell supersymmetric or Gauss-Bonnet) were used, whichgive the entropies agreeing (at best) just for BPS black holes. The keyproperty of the solutions, which enabled us to tackle the action containinginfinite number of terms, is vanishing of the Riemann tensor \bar{R}_{MNPQ}obtained from torsional connection defined with \bar{\Gamma} = \Gamma - H/2.Morover, if every monomial of the remaining part of the effective action wouldcontain at least two Riemanns \bar{R}_{MNPQ}, it would trivially follow thatour solutions are exact solutions of the full heterotic effective action inD=10. The above conjecture, which appeared (in this or stronger form) from timeto time in the literature, has controversial status, but is supported by themost recent calculations of Richards (arXiv:0807.3453 [hep-th]). Agreement ofour results for the entropies with the microscopic ones supports theconjecture. As for small black holes, our solutions in D=5 still have singularhorizons.

alpha'-exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry