All static spherical axion-dilaton solutions are SL(2,R) images of the FJNW seed, and scalar hair increases the alpha-prime curvature diagnostic at the string-black-hole correspondence surface, selecting the hairless Schwarzschild branch as the only controlled one.
Chandrasekhar, The Mathematical Theory of Black Holes, Oxford Univ
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Scalar Hair at the String-Black-Hole Correspondence
All static spherical axion-dilaton solutions are SL(2,R) images of the FJNW seed, and scalar hair increases the alpha-prime curvature diagnostic at the string-black-hole correspondence surface, selecting the hairless Schwarzschild branch as the only controlled one.