Hawking Radiation Power Equations for Black Holes

TL;DR

This paper derives Hawking radiation power equations for various black hole types using greybody factors, revealing how power depends on temperature, horizon radius, and frequency in different asymptotic geometries.

Contribution

It provides new derivations of Hawking radiation power equations for asymptotically flat, AdS, and dS black holes, highlighting frequency and geometry dependencies.

Findings

Power depends on temperature and horizon radius at low frequency for flat black holes.

At high frequency, power depends only on Hawking temperature.

Power equations are consistent across different AdS black hole solutions.

Abstract

We derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes, This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black holes both below and above the critical frequency. The radiation power equation for at asymptotic frequency is same for both Schwarzschild AdS and Reissner-Nordstr\"om AdS solutions and only depends on the Hawking temperature. We also discuss the power equation for asymptotically dS black holes at low frequency, for both even or odd dimensions.