Hawking Radiation Spectra for Scalar Fields by a Higher-Dimensional Schwarzschild-de-Sitter Black Hole

TL;DR

This paper analyzes scalar field propagation and Hawking radiation spectra in higher-dimensional Schwarzschild-de-Sitter black holes, revealing how non-minimal coupling and extra dimensions influence emission rates and energy distribution between bulk and brane channels.

Contribution

It provides exact numerical calculations of greybody factors and Hawking spectra for scalar fields with non-minimal coupling in higher-dimensional black hole backgrounds, highlighting the dominance of bulk emission.

Findings

Non-minimal coupling suppresses energy emission rates.

Cosmological constant influences Hawking radiation profiles.

Bulk emission dominates over brane emission in certain regimes.

Abstract

In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de-Sitter black hole as well as on the projected-on-the-brane 4-dimensional background. The scalar fields have also a non-minimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then proceed to derive the Hawking radiation spectra for a higher-dimensional Schwarzschild-de-Sitter black hole, and we study both bulk and brane channels. We demonstrate that the non-minimal field coupling, that creates an effective mass term for the fields, suppresses the energy emission rates while the cosmological constant assumes a dual role. By computing the relative energy rates and the total emissivity ratio for bulk and brane emission, we demonstrate that the combined effect of a large number of extra dimensions and value of the field coupling gives to the bulk channel the clear domination in the bulk-brane energy balance.