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We study the thermodynamical and geometrical behaviour of the black holes that arise as solutions of the heterotic string action. We discuss the near-horizon scaling behaviour of the solutions that are described by two-dimensional Anti-de Sitter Space AdS(2). We find that finite-energy excitations of AdS(2) are suppressed only for scaling limits characterised by a dilaton which is constant near the horizon, whereas this suppression does not occur when the dilaton is non constant.

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