Recent works have revealed that matching conditions play a major role on general consistency properties of relativistic fluid dynamics such as causality, stability and wellposedness of the equations of motion. In this paper we derive transient fluid dynamics from kinetic theory, using the method of moments as proposed by Israel and Stewart, without imposing an specific matching condition. We then investigate how the equations of motion and their corresponding transport coefficients are affected by the choice of matching condition.
I. INTRODUCTIONRelativistic fluid dynamics is an effective theory derived to describe the long-distance, long-time dynamics of a given microscopic theory. It is applied in several fields of physics, from the description of neutron star mergers [1,2] to the hot and dense nuclear matter produced in ultra-relativistic heavy ion collisions [3][4][5]. Nevertheless, the theoretical foundations of relativistic dissipative fluid dynamics remain open, still being topic of intense investigation [6,7].Relativistic generalizations of Navier-Stokes theory display physical and mathematical pathologies which practically prevents its use in general applications. The main issue is that Navier-Stokes theory is acausal and displays intrinsic instabilities [8] when perturbed around a global equilibrium state -an illness that cannot be corrected by adjusting matching conditions or transport coefficients. An early attempt to derive a linearly causal and stable fluid-dynamical theory was put forward by Israel and Stewart in the 1970's [9, 10]. The main feature of Israel-Stewart theory is that, instead of imposing constitutive relations relating the dissipative currents with derivatives of the velocity field, they promoted the non-equilibrium fields to independent dynamical variables for which they derived relaxation equations. Then, the requirements of linear causality and stability yield constrains on the relaxation times that are allowed in the formulation [11][12][13][14]. Even so, in Israel-Stewart theories, existence and uniqueness of solutions are not guaranteed in general curved spaces [15].Recently, Bemfica, Disconzi and Noronha proposed a novel theory of fluid dynamics which is not derived following the procedure outlined by . Other aspects about this formulation were also investigated in Refs. [18,19]. In this approach, fluid dynamics is constructed from a generalized gradient expansion, which includes both time-like and space-like gradients. This is in contrast to the traditional approach, used to derive Navier-Stokes theory, which consists of an expansion only in space-like gradients. It was then demonstrated that a first order theory in such generalized gradient expansion can lead to a causal and linearly stable theory as long as appropriate matching conditions are imposed.Matching conditions are constraints required to define the local equilibrium state of a fluid in the presence of dissipation, i.e., they define the temperature, chemical potential, and velocity of a viscous fluid. These conditi...