Black-Body Radiation in a Uniformly Accelerated Frame

TL;DR

This paper derives how black-body radiation appears to a uniformly accelerated observer, revealing that the spectrum is time-dependent, position-dependent, and affected by acceleration, leading to phenomena like red/blue shifts and mode creation or annihilation.

Contribution

It introduces a derivation of Planck's law in Rindler coordinates, showing the influence of acceleration on black-body spectra and observer perception, including emissivity scaling and threshold effects.

Findings

Spectrum is time-dependent and scaled by position and acceleration.

Observer perceives black-body as black, hyperblack, or grey depending on conditions.

Radiation modes are red or blue-shifted over time, with possible creation or annihilation.

Abstract

We derive Planck's radiation law in a uniformly accelerated frame expressed in Rindler coordinates. The black-body spectrum is time-dependent by its temperature and Planckian at each instantaneous time, but it is scaled by an emissivity factor that depends on the Rindler spatial coordinate and the acceleration magnitude. The observer in an accelerated frame will perceive the black-body as black, hyperblack, or grey, depending on its position with respect to the source (moving away or towards), the acceleration magnitude, and the case of whether it is accelerated or decelerated. For an observer accelerating away from the source, there exists a threshold on the acceleration magnitude beyond which it stops receiving radiation from the black-body. Since the frequency and the number of modes in Planck's law evolve over time, the spectrum is continuously red or blue-shifted towards lower (or higher) frequencies as time progresses, and the radiation modes (photons) could be created or annihilated, depending on the observer's position and its acceleration or deceleration relative to the source of radiation.