Abstract
There has been much work on explaining Hawking radiation as a quantum tunneling process through horizons. Basically, this intuitive picture requires the calculation of the imaginary part of the action for outgoing particle. And two ways are known for achieving this goal: the null-geodesic method and the Hamilton–Jacobi method. We apply these methods to the charged black holes in 2D dilaton gravity which is originated from the low energy effective theory of type 0A string theory. We derive the correct Hawking temperature of the black holes including the effect of the back reaction of the radiation, and obtain the entropy by using the 1st law of black hole thermodynamics. For fixed-charge ensemble, the 0A black holes are free of phase transition and thermodynamically stable regardless of mass-charge ratio. We show this by interpreting the back reaction term as the inverse of the heat capacity of the black holes. Finally, the possibility of the phase transition in the fixed-potential ensemble is discussed.
Highlights
Since Hawking proved that black holes can radiate thermally [1], it is believed that the black holes are kinds of a thermal system and have thermodynamic relations among the quantities describing black holes
In this paper we explored the thermodynamic properties of the 0A black holes by using the tunneling picture
We found the heat capacity of the 0A black holes from the back reaction effect which is related to the ω2 term in the action
Summary
Since Hawking proved that black holes can radiate thermally [1], it is believed that the black holes are kinds of a thermal system and have thermodynamic relations among the quantities describing black holes. There have been much works applying this method to various types of black holes.(See the references in [7]) The essential idea is that the positive energy particle created just inside the horizon can tunnel through the geometric barrier quantum mechanically. It is observed as the Hawking flux at infinity. We apply these two methods to the charged black holes in two dimensional dilaton gravity which is originated from the low energy effective theory of the 0A string theory.
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