Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point has its origins in work dating from the 1950s, but its…
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Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars…

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of special…

Steady accretion disks are considered, and attention is given to the role of viscosity, radiation mechanisms, time dependence, instability, variability, and the inner boundary in the physics of accretion disks. The major uncertainties in accretion…

We present the piecewise parabolic method, a higherorder extension of Godunov's method. There are several new features of this method which distinguish it from other higherorder Godunovtype methods. We use a higherorder spatial interpolation…

We have recently presented an investigation in full general relativity of the dynamics and gravitationalwave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus (see arXiv:0804.0594). We here…

This article presents a comprehensive overview of numerical hydrodynamics and magneto hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000,…

We discuss the cosmological simulation code GADGET2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the Nbody method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of…

We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar…

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general postNewtonian sources. The…

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a longstanding unsolved problem in theoretical physics. Blackhole mergers are monumental astrophysical events, releasing tremendous…

The expansion of the field equations of general relativity in powers of the gravitational coupling constant yields conservation laws of energy, momentum, and angular momentum. From these, the loss of energy and angular momentum of a system due to…

Hydrodynamic cosmological simulations at present usually employ either the Lagrangian SPH technique, or Eulerian hydrodynamics on a Cartesian mesh with adaptive mesh refinement. Both of these methods have disadvantages that negatively impact their…

We report on the completion of the first version of a newgeneration simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains…

Two classes of Xray pulsars, the Anomalous Xray Pulsars and the Soft Gammaray Repeaters, have been recognized in the last decade as the most promising candidates for being magnetars: isolated neutron stars powered by magnetic energy. I review the…

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within…

Rotating relativistic stars are receiving significant attention in recent years, because of the information they can yield about the equation of state of matter at extremely high densities and because they are one of the more possible sources of…

Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of probing with observations of such compact objects some of the most intriguing General…

We discuss various aspects of the postNewtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive postNewtonian equations of motion for relativistic compact binaries based…

We present a new threedimensional fully generalrelativistic hydrodynamics code using highresolution shockcapturing techniques and a conformal traceless formulation of the Einstein equations. Besides presenting a thorough set of tests which the…
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