  Based on the formalism of nonlocal extension of the Israel-Stewart causal
thermodynamics on the one hand, and on the formalism of the extended
thermostatics on the other hand, we propose the new model of nonlocal
relativistic non-equilibrium thermostatics for description of the static
spherically symmetric stellar systems. This nonlocal formalism operates with
the pair of orthogonal four-vectors: one of them is the standard unit timelike
medium velocity four-vector, the second one is the unit spacelike director. We
derived the extended equation describing the profile of the non-equilibrium
pressure, which can be indicated as the static analog of the Burgers
constitutive equation known in classical rheology.
