Noncovariant parabolic theories of relativistic diffusion

Abstract

A new first-order theory of relativistic dissipation has been recently proposed, where viscous effects are incorporated using the traditional Navier-Stokes framework. Its main novelty is the avoidance of dynamical instabilities by allowing different observers to use equations that are not related by exact Lorentz transformations. In this work, we explore the implications of this non-covariance in depth. In particular, we discuss how predictions differ between observers moving at nearly luminal speeds relative to each other. We find that all disagreements stem from the relativity of simultaneity, which introduces frame-dependent anisotropic delays in the diffusive process. These anisotropies significantly limit the applicability of the equation used by observers who move very fast relative to the medium. However, the magnitude of the related error remains finite at infinite Lorentz factors, meaning that it is possible to find a regime where all observers agree on the outcome of experiments.

14 pages, 5 captioned figures, published on PRD (see https://journals.aps.org/prd/abstract/10.1103/ppy5-654c)

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Cited by in corpus (4)

• Heat propagation in rotating relativistic bodies
• The initial data of effective field theories of relativistic viscous fluids and gravity
• Lorentz-boosted diffusion: initial value formulation and exact solutions
• The diffusion equation is compatible with special relativity