Preface

Summary

We are convinced of a genuine need for a monograph describing the many facets and new developments in numerical relativistic hydrodynamics. Such calculations are crucial to several areas of current research in the physics of stellar collapse, supernovae, and black hole formation, as well as the merging of the final orbits of coalescing binary neutron stars. Both problems are only now entering the level of sophistication where three-dimensional relativistic hydrodynamics simulations are both possible and necessary. In the former problem such calculations are crucial to understand the explosion mechanism. In the latter problem, a great deal of interest in such calculations has recently been inspired by the development of next-generation gravity wave detectors to search for such events, and as a possible explanation of the physics underlying observed astrophysical γ-ray bursts.

The field of numerical relativistic hydrodynamics has developed over the past 30 years, but there has not been written a technical text explaining the many techniques relevant to this discipline, many of which are much different than standard general relativity textbook approaches. This book will present such a review of techniques for numerical general relativistic hydrodynamics developed by one of the pioneers of this field over the past three decades.

We begin by developing the equations and differencing schemes for special relativistic hydrodynamics as an introduction to the metric formulation of the problems. Here, the basic numerical techniques and a number of test problems and applications will be discussed.

Following this, the formalism for matter flows in the curved spacetime of general relativity will be presented in the usual (3+1) formalism.