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Tachyon Perturbation on Two Dimensional Black Hole

We study the geometry of the two dimensional string theoretic black hole under tachyonic perturbations. These perturbations are restricted to affect only the metric and the dilaton, while other string theoretic excitations (like the axion) are ignored. The metric and linearized dilaton perturbations are determined to lowest non-trivial order of the tachyonic hair in the presence of back reaction. We evaluate the Kretschmann scalar and argue that the horizon does not become singular in the presence of tachyon perturbations (to the order of our consideration). A closed-form solution of the allowed tachyon field and that of the allowed tachyon potential emerges as a requirement of self-consistency of our solution.