Presents a powerful new framework for out-of-equilibrium hydrodynamics, with connections to kinetic theory, AdS/CFT and applications to high-energy particle collisions.

The past decade has seen unprecedented developments in the understanding of relativistic fluid dynamics in and out of equilibrium, with connections to astrophysics, cosmology, string theory, quantum information, nuclear physics and condensed matter physics. Romatschke and Romatschke offer a powerful new framework for fluid dynamics, exploring its connections to kinetic theory, gauge/gravity duality and thermal quantum field theory. Numerical algorithms to solve the equations of motion of relativistic dissipative fluid dynamics as well as applications to various systems are discussed. In particular, the book contains a comprehensive review of the theory background necessary to apply fluid dynamics to simulate relativistic nuclear collisions, including comparisons of fluid simulation results to experimental data for relativistic lead-lead, proton-lead and proton-proton collisions at the Large Hadron Collider (LHC). The book is an excellent resource for students and researchers working in nuclear physics, astrophysics, cosmology, quantum many-body systems and string theory.

This book provides an introduction to relativistic dissipative fluid dynamics, with particular emphasis on its derivation from microscopic transport theory. After a phenomenological derivation of relativistic dissipative fluid dynamics from the second law of thermodynamics, the intrinsic instabilities of relativistic Navier-Stokes theory are discussed. In turn, analytical solutions of relativistic dissipative fluid dynamics are presented. Following, the authors discuss several theories and approaches to derive transport coefficients in dissipative fluid dynamics such as the Chapman-Enskog theory, the theory of Israel and Stewart, and a more recent derivation of relativistic dissipative fluid dynamics based on kinetic theory, which constitutes the main focus of the second part of this book. This book is intended for advanced graduate students and researchers in physics and requires basic knowledge of the theory of special and general relativity. It should be of particular interest to researchers that apply relativistic fluid dynamics in cosmology, astrophysics, and high-energy nuclear physics.

Pham Mau Quam: Problèmes mathématiques en hydrodynamique relativiste.- A. Lichnerowicz: Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes.- A.H. Taub: Variational principles in general relativity.- J. Ehlers: General relativistic kinetic theory of gases.- K. Marathe: Abstract Minkowski spaces as fibre bundles.- G. Boillat: Sur la propagation de la chaleur en relativité.

This book treats the classical problem of gravitational physics within Einstein's theory of general relativity. It presents basic principles and equations needed to describe rotating fluid bodies, as well as black holes in equilibrium. It then goes on to deal with a number of analytically tractable limiting cases, placing particular emphasis on the rigidly rotating disc of dust. The book concludes by considering the general case using powerful numerical methods that are applied to various models, including the classical example of equilibrium figures of constant density. Researchers in general relativity, mathematical physics, and astrophysics will find this a valuable reference book on the topic. A related website containing codes for calculating various figures of equilibrium is available at www.cambridge.org/9781107407350.

In recent years the subject of relativistic fluid dynamics has found substantial applications in astrophysics and cosmology (theories of gravitational collapse, models of neutron stars, galaxy formation), as well as in plasma physics (relativistic fluids have been considered as models for relativistic particle beams) and nuclear physics (relativistic fluids are currently used in the analysis of the heavy ion reactions). Modern methods of analysis and differential geometry have now also been introduced. The International C.I.M.E. Course brought together expertise and interest from several areas (astrophysics, plasma physics, nuclear physics, mathematical methods) to create an appropriate arena for discussion and exchange of ideas. The main lecture courses introduced the most significant aspects of the subject and were delivered by leading specialists. The notes of these have been written up for this volume and constitute an up-to-date and thorough treatment of these topics. Several contributions from the seminars on specialized topics of complementary interest to the courses are also included.