Effect of the Born-Infeld Parameter in higher dimensional Hawking radiation

TL;DR

This paper investigates how the Born-Infeld parameter influences Hawking radiation in higher dimensional linear dilaton black holes, confirming temperature calculations and exploring the effects of dimensionality and field types on radiation properties.

Contribution

It extends the semi-classical radiation spectrum analysis to higher dimensions and various theories, demonstrating the impact of the Born-Infeld parameter and dimensionality on Hawking temperature.

Findings

Hawking temperature matches surface gravity calculations in higher dimensions.

Higher dimensions affect the value of Hawking temperature explicitly.

Black holes interpolate between different field solutions by varying the Born-Infeld parameter.

Abstract

We show in detail that the Hawking temperature calculated from the surface gravity is in agreement with the result of exact semi-classical radiation spectrum for higher dimensional linear dilaton black holes in various theories. We extend the method derived first by Cl\'ement-Fabris-Marques for 4-dimensional linear dilaton black hole solutions to the higher dimensions in theories such as Einstein-Maxwell-Dilaton, Einstein-Yang-Mills-Dilaton and Einstein-Yang-Mills-Born-Infeld-Dilaton. Similar to the Cl\'ement-Fabris-Marques results, it is proved that whenever an analytic solution is available to the massless scalar wave equation in the background of higher dimensional massive linear dilaton black holes, an exact computation of the radiation spectrum leads to the Hawking temperature T_{H} in the high frequency regime. The significance of the dimensionality on the value of T_{H} is shown, explicitly. For a chosen dimension, we demonstrate how higher dimensional linear dilaton black holes interpolate between the black hole solutions with Yang-Mills and electromagnetic fields by altering the Born-Infeld parameter in aspect of measurable quantity T_{H}. Finally, we explain the reason of, why massless higher dimensional linear dilaton black holes cannot radiate.