Hawking radiation as perceived by different observers: An analytic expression for the effective-temperature function

TL;DR

This paper derives a general analytic expression for the effective-temperature function in black hole spacetimes, showing how different observers perceive Hawking radiation based on their position, velocity, and acceleration.

Contribution

It provides a unified formula for the effective-temperature function, expanding previous case-by-case analyses to a comprehensive, physically interpretable expression.

Findings

The formula accounts for vacuum state, observer position, velocity, and acceleration.

Illustrative examples demonstrate the application of the formula.

The expression enhances understanding of observer-dependent Hawking radiation perception.

Abstract

Given a field vacuum state in a black hole spacetime, this state can be analysed in terms of how it is perceived (in terms of particle content) by different observers. This can be done by means of the effective-temperature function introduced by Barcel\'o et al. in [1]. In Barbado et al. [2], this function was analysed in a case by case basis for a number of interesting situations. In this work, we find a general analytic expression for the effective-temperature function which, apart from the vacuum state choice, depends on the position, the local velocity and the acceleration of the specific observer. We give a clear physical interpretation of the quantities appearing in the expression, and illustrate its potentiality with a few examples.