Spectral Universality of Turbulent Fluctuations in Relativistic Flows

TL;DR

This paper introduces a Lorentz-covariant method to relate spacetime and temporal spectra in relativistic turbulence, revealing a universal scaling relation that holds under certain conditions.

Contribution

It develops a covariant framework for spectral analysis in relativistic flows and derives a universal scaling law for self-similar spectra.

Findings

Universal spectral scaling relation $ ext{α} = ext{β} - D$ for self-similar spectra

Breakdown of universality when spacetime homogeneity is violated

Temporal spectra are nonlocal observables in relativistic flows

Abstract

We develop a Lorentz-covariant framework for projecting spacetime spectra into temporal spectra of stationary turbulent fluctuations in relativistic flows. For self-similar spacetime spectra, we derive a universal scaling relation, $\alpha = \beta - D$, where $\alpha$ is the temporal spectral index, $\beta$ the spacetime homogeneity exponent, and $D$ the effective dimensionality of spectral support. We further demonstrate that this universality breaks down when spacetime homogeneity is violated. Temporal spectra in relativistic flows are thus intrinsically nonlocal observables, requiring a covariant projection framework that establishes a general principle for spectral inference in relativistic plasma turbulence and high-energy plasma flows.