Causal Energy-Momentum Tensors and Relativistic Fluids

TL;DR

This paper proves that in causal, bounded, and diffeomorphism-invariant theories, the energy-momentum tensor of relativistic fluids depends only on a finite number of covariant derivatives of the fields, ensuring locality.

Contribution

It establishes a general result linking causality and invariance to the finite derivative dependence of the energy-momentum tensor in relativistic theories.

Findings

Energy-momentum tensor depends on finite covariant derivatives

Causality constrains the form of the energy-momentum tensor

Theoretical framework applies to general relativistic fluids

Abstract

In this paper, we consider a theory defined by an energy-momentum tensor depending on a set of general fields, including the space-time metric. We prove that if the theory is causal, bounded and transforms appropriately under diffeomorphism, it will depend only on the local values of the independent fields and their covariant derivatives up to a finite order. The implications are that the energy-momentum tensor of a causal relativistic fluid can only depend on covariant derivatives only up to a finite order.