### 5.6 Characteristic speeds in a viscous, heat-conducting gas

We recall from Section 2.4, in particular (14), that the jumps across acceleration waves and their
speeds of propagation are to be calculated from the homogeneous system
In the present context, where the field equations are given by (79, 80) this homogeneous algebraic system
spreads out into three equations, viz.
By (89) and (91) this is a fully explicit system, if the thermal equation of state is known.
The vanishing of its determinant determines the characteristic speeds. Seccia & Strumia [44] have
calculated these speeds – one transversal and two longitudinal ones – for non-degenerate gases and obtained
the following results in the non-relativistic and ultra-relativistic cases
All speeds are finite and smaller than c. Inspection shows that in the non-relativistic limit the order of
magnitude of these speeds is that of the ordinary speed of sound, while in the ultra-relativistic case the
speeds come close to c.