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We derive a first-order, stable and causal, relativistic hydrodynamic theoryfrom the microscopic kinetic equation using the gradient expansion technique ina general frame. The general frame is introduced from the arbitrary matchingconditions for hydrodynamic fields. The interaction is introduced in therelativistic Boltzmann equation through the momentum-dependent relaxation timeapproximation (MDRTA) with the proposed collision operator that preserves theconservation laws. We demonstrate here for the first time that not only thegeneral frame choice, but also the momentum dependence of microscopicinteraction rate, captured through MDRTA, is imperative for producing theessential field corrections that give rise to a causal and stable first-orderrelativistic theory.

Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?