Post-Newtonian Hydrodynamics

This book introduces and develops post-Newtonian kinetic and phenomenological theories in a self-contained manner. The starting point for phenomenological theory is Einstein's field equations from which the first and second post-Newtonian approximations are derived. Within phenomenological theory, Eulerian hydrodynamic equations are obtained and the conservation laws are derived. The kinetic counterpart of the theory is developed within the framework of Boltzmann equation, where the post-Newtonian equilibrium distribution function and the hydrodynamic equations are determined. Some astrophysical applications of post-Newtonian hydrodynamic equations, such as stellar structure models for stars, the spherically symmetrical accretion of a gas into a massive object, the Jeans instability (which is responsible for the collapse of interstellar gas clouds), and the galaxy rotation curves, are presented and the importance of post-Newtonian corrections is discussed. This book will be helpful not only as a text for advanced courses, but also as a reference for physicists, astrophysicists, and applied mathematicians who are interested in the phenomenological and kinetic post-Newtonian theory and its applications.