4 Relativistic Fluid Flow

In many radiation hydrodynamics problems of astrophysical interest, the fluid moves at extremely high velocities, and relativistic effects become important. Examples of such flows are supernova explosions, the cosmic expansion, and solar flares, To account for relativistic effects on a macros-copic level, it is usually adequate to adopt a continuum view, without inquiring in ” detail into the nature of the fluid itself; such an approach is obviously approp~-iate for a high-velocity flow of moderate-temperature, low-density gas. In some cases, however, the fluid exhibits relativistic effects on a microscopic level. These situations require a kinetic theory approach, which, in addition, has the advantage of providing precise definitions of, and relations among, the thermodynamic properties of the m ateri al. in what follows we shall develop both the continuum and kinetic theory views of the dynamics of relativistic ideal fluids, thereby retaining parallel-ism with our earlier work in the nonrelativistic limit, while at the same time laying a thorough groundwork for the treatment of radiation in Chapters 6 and 7. For relativistic nonideal fluids, we consider the continuum view only, obtaining covariant generalizations of the results in Chapter 3. The flows that are of primary importance to us in this book can be treated entirely within the framework of special relativity. Nevertheless, many of the equations derived in this chapter are completely covariant and apply in general relativity. Only in $S95 and 96 will we need to forsake inertial frames and work in a Rieman nian spacetime. Excellent accounts of the theory of general relativistic flows are given in (L4); Chapters 5, 22, and 26 of (M3); (Tl); and Chapter 11 of (W2). Numerical methods for solving general-relativistic flow problems are discussed in (Ml), (M2), and (W3). 4.1 Basic Concepts of Special Relativity In this section we summarize the ideas from special relativity needed to obtain the equations of hydrodynamics in covariant form. For a more complete discussion the reader can consult the many texts available [e.g.