  Effective theory arguments are used to derive the most general
energy-momentum tensor of a relativistic viscous fluid with an arbitrary
equation of state (in the absence of other conserved currents) that is
first-order in the derivatives of the energy density and flow velocity and does
not include extended variables such as in Mueller-Israel-Stewart-like theories.
This energy-momentum tensor leads to a causal theory, provided one abandons the
usual conventions for the out-of-equilibrium hydrodynamic variables put forward
by Landau-Lifshitz and Eckart. In particular, causality requires nonzero
out-of-equilibrium energy density corrections and heat flow. Conditions are
found to ensure linear stability around equilibrium in flat space-time. We also
prove local existence and uniqueness of solutions to the equations of motion.
Our causality, existence, and uniqueness results hold in the full nonlinear
regime, without symmetry assumptions, in four space-time dimensions, with or
without coupling to Einstein's equations, and are mathematically rigorously
established. Furthermore, a kinetic theory realization of this energy-momentum
tensor is also provided.
