Mirror effect induced by the dilaton field on the Hawking radiation

A “stringy particle” action is naturally derived from Kaluza‐Klein compactification of a test string action coupled to the dilaton field in a conformally invariant manner. According to the standard procedure, we perform the second quantization of the stringy particle. As an interesting application, we consider evaporation of a near‐extremal dilatonic black hole by Hawking radiation via the stringy particles. We show that a mirror surface which reflects them is induced by the dilaton field outside the the horizon when the size of the black hole is comparable to the Planck scale. As a result, the energy flux does not propagate across the surface, and hence the evaporation of the dilatonic black hole stops just before the naked singularity at the extremal state appears even though the surface gravity is non‐zero in the extremal limit.