Spectral Universality of Turbulent Fluctuations 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.