Hawking radiation received at infinity in higher dimensional Reissner-Nordstr\"om black hole spacetimes

TL;DR

This paper numerically analyzes Hawking radiation transmission in higher-dimensional Reissner-Nordström black holes, revealing dimension-dependent effects on radiation spectra and implications for black hole evaporation rates.

Contribution

It extends the study of Hawking radiation transmission to higher dimensions, providing numerical results on frequency-dependent transmission rates and their sensitivity to spacetime dimension and black hole parameters.

Findings

Transmission coefficients vanish at low frequencies.

Transmission increases with frequency and saturates.

Higher dimensions show slower convergence and more significant quantum number effects.

Abstract

In this work, we investigate the Hawking radiation in higher dimensional Reissner-Nordstr\"om black holes as received by an observer, resides at infinity. The frequency-dependent transmission rates, which deform the thermal radiation emitted in the vicinity of the black hole horizon, are evaluated numerically. Apart from the case of four-dimensional spacetime, the calculations are extended to higher dimensional Reissner-Nordstr\"om metrics, and the results are found to be somewhat sensitive to the spacetime dimension. In general, it is observed that the transmission coefficients practically vanishes when the frequency of the emitted particle approaches zero. It increases with increasing frequency and eventually saturates to some value. For four-dimensional spacetime, the above result is shown to be mostly independent of the metric's parameter, neither of the orbital quantum number of the particle, once the location of the event horizon, $r_h$, and the product of the charges of the black hole and the particle $qQ$ are given. For higher-dimensional cases, on the other hand, the convergence becomes more slowly. Moreover, the difference between states with different orbital quantum numbers is found to be more significant. As the magnitude of the product of charges $qQ$ becomes more significant, the transmission coefficient exceeds one. In other words, the resultant spectral flux is amplified, which results in an accelerated process of black hole evaporation. The relation between the calculated outgoing transmission coefficient with existing results on the greybody factor is discussed.