We review the current status of general relativistic studies for coalescences of black hole–
neutron star binaries. First, high-precision computations of black hole–neutron star binaries …

Understanding the predictions of general relativity for the dynamical interactions of two black
holes has been a long-standing unsolved problem in theoretical physics. Black-hole …

We perform numerical simulations of a three-dimensional (3D) time evolution of pure
gravitational waves. We use a conformally flat and K= 0 initial condition for the evolution of …

This book introduces the modern field of 3+ 1 numerical relativity. The book has been written
in a way as to be as self-contained as possible, and only assumes a basic knowledge of …

We present a new formulation of the Einstein equations that casts them in an explicitly first
order, flux-conservative, hyperbolic form. We show that this now can be done for a wide …

Canonical methods are a powerful mathematical tool within the field of gravitational
research, both theoretical and experimental, and have contributed to a number of recent …

Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the
emphasis on local solutions of the evolution equations. Particular attention is payed to giving …

A general-covariant extension of Einstein's field equations is considered with a view to
numerical relativity applications. The basic variables are taken to be the metric tensor and …

Numerical relativity is the most promising tool for theoretically modeling the inspiral and
coalescence of neutron star and black hole binaries, which, in turn, are among the most …

This paper presents both a numerical method for general relativity and an application of that
method. The method involves the use of harmonic coordinates in a 3+ 1 code to evolve the …