Effect of the cosmological constant in the Hawking radiation of 3D charged dilaton black hole

TL;DR

This paper analyzes the Hawking radiation spectrum of 3D charged dilaton black holes with a cosmological constant, revealing how the cosmological constant influences the temperature at different frequency regimes.

Contribution

It provides an exact solution for the wave equation and derives the Hawking temperature considering the effects of charge and the cosmological constant.

Findings

Radiation spectrum matches the Hawking temperature for uncharged black holes.

Charged black holes' temperature is determined at low frequencies, emphasizing the role of the cosmological constant.

Exact hypergeometric solutions enable precise spectral analysis.

Abstract

This paper deals with the semiclassical radiation spectrum of static and circularly symmetric 3D charged dilaton black holes with cosmological constant {\Lambda} in non-asymptotically flat spacetimes. We first review the 3D charged dilaton black holes which are solution to low-energy string action. The wave equation of a massless scalar field is shown to be exactly solvable in terms of hypergeometric functions. Thus, the radiation spectrum and its corresponding temperature are obtained, precisely. Computations at high frequency regime show that the radiation spectrum yields the Hawking temperature of the black hole with no charge. Unlike the chargeless case, the Hawking temperature of the charged dilaton black holes is derived from the radiation spectrum at the low frequencies. The utmost importance of the {\Lambda} in the latter result is highlighted.