Bulk and Brane Decay of a (4+n)-Dimensional Schwarzschild-De-Sitter Black Hole: Scalar Radiation

TL;DR

This study analyzes Hawking radiation from higher-dimensional Schwarzschild-de-Sitter black holes, revealing how spacetime curvature and extra dimensions influence scalar emission spectra through analytical and numerical methods.

Contribution

It extends Hawking radiation analysis to include spacetime curvature effects, providing detailed calculations of greybody factors in higher-dimensional de Sitter backgrounds.

Findings

Energy emission increases with spacelike dimensions at high energies.

Cosmological constant causes a constant emission rate of ultrasoft quanta.

Results apply to small black holes in extra-dimensional and de Sitter spacetimes.

Abstract

In this paper, we extend the idea that the spectrum of Hawking radiation can reveal valuable information on a number of parameters that characterize a particular black hole background - such as the dimensionality of spacetime and the value of coupling constants - to gain information on another important aspect: the curvature of spacetime. We investigate the emission of Hawking radiation from a D-dimensional Schwarzschild-de-Sitter black hole emitted in the form of scalar fields, and employ both analytical and numerical techniques to calculate greybody factors and differential energy emission rates on the brane and in the bulk. The energy emission rate of the black hole is significantly enhanced in the high-energy regime with the number of spacelike dimensions. On the other hand, in the low-energy part of the spectrum, it is the cosmological constant that leaves a clear footprint, through a characteristic, constant emission rate of ultrasoft quanta determined by the values of black hole and cosmological horizons. Our results are applicable to "small" black holes arising in theories with an arbitrary number and size of extra dimensions, as well as to pure 4-dimensional primordial black holes, embedded in a de Sitter spacetime.