Tachyon Perturbation on Two Dimensional Black Hole

TL;DR

This paper investigates how tachyonic perturbations influence the geometry of two-dimensional string theory black holes, showing that the horizon remains non-singular and deriving self-consistent solutions for the tachyon field and potential.

Contribution

It provides the first analysis of tachyon perturbations affecting only metric and dilaton in 2D black holes, with explicit solutions ensuring self-consistency.

Findings

Horizon remains non-singular under tachyon perturbations

Explicit solutions for tachyon field and potential derived

Perturbations do not induce horizon singularities to lowest order

Abstract

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.