Frame transformation and stable-causal hydrodynamic theory

Abstract

In this work, a connection has been indicated between the different existing formulations of relativistic hydrodynamic theories, which, in order to be causal and stable, (i) either requires `non-fluid' variables apart from velocity and temperature to be promoted to new degrees of freedom, or, (ii) needs to be in a generalized hydrodynamic frame other than those given by Landau or Eckart. The BDNK stress tensor (originally in a general frame) has been rewritten in the Landau frame using linearized all-order gradient-corrected redefinitions of the temperature and velocity fields. The redefinitions indicate that, while the BDNK formalism has a finite number of derivatives in the general frame, when written in the Landau frame, it either has an infinite number of derivatives, or one has to introduce MIS-like `non-fluid' variables by summing the infinite number of derivatives in the field redefinitions. There can be non-unique ways of performing these infinite-order summations. Finally, the dispersion relations and the corresponding spectra of these different systems of MIS type equations have been analyzed to check that the systems of equations presented here are indeed equivalent to the BDNK formalism, at least in the hydrodynamic regime.