Causal Energy-Momentum Tensors and Relativistic Fluids

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.