Hawking Radiation in a Plebanski-Demianski Black Hole

TL;DR

This paper calculates Hawking radiation flux from a Plebański-Demiański black hole using anomaly methods, emphasizing the importance of the consistent anomaly approach in de Sitter space with a cosmological constant.

Contribution

It demonstrates the application of the consistent anomaly method to derive Hawking radiation in a complex black hole spacetime including a cosmological constant, ensuring valid results in de Sitter space.

Findings

Validated the consistent anomaly method for Hawking flux calculations.

Reproduced known results in limiting cases for verification.

Highlighted the inadequacy of the covariant anomaly method in this context.

Abstract

In this paper, we show the flux of Hawking radiation in a Pleba\'nski-Demia\'nski black hole from the point of view of gauge and gravitational anomalies. We will use the consistent anomaly method to guarantee that our results are valid in the de Sitter space. This is because we are including the cosmological constant into our parameters and the covariant anomaly method gives a wrong value for the Hawking temperature. We also show that these calculations are a general result. In order to verify the consistence of our results, we can reproduce earlier known results as certain limiting cases.