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A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented.

We have modeled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating axisymmetric n = 1/2 polytropic star with a ratio of rotational to gravitational potential energy T/ img1.gif = 0.181 is driven by GRR forces to a barlike structure, as predicted by linear theory. The pattern frequency of the bar slows to nearly zero, that is, the bar becomes almost stationary as viewed from an inertial frame of reference as GRR removes energy and angular momentum from the star. In this "Dedekind-like" state, rotational energy is stored as motion of the fluid in highly noncircular orbits inside the bar. However, in less than 10 dynamical times after its formation the bar loses its initially coherent structure as the ordered flow inside the bar is disrupted by what appears to be a purely hydrodynamic short-wavelength "shearing"-type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented.

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple relativistic Navier–Stokes descriptions of these states. Thus, for example, in the relaxed form of a physical fluid state the stress energy tensor is in effect indistinguishable from a perfect fluid stress tensor plus small dissipative corrections proportional to the shear of the fluid velocity, the gradient of the temperature, etc.

Abstract: This paper completes the proof of the necessity of spherical symmetry in the static general-relativistic stellar models that have equations of state satisfying certain inequalities. The technical assumption — that there exists a ldquoreference spherical stellar modelrdquo — that was essential in the previous discussions of this problem is removed. This paper also extends beyond previous discussions the class of equations of state included in the proof. The analysis of the equations for spherical stellar models, used here to demonstrate the existence of a ldquoreference spherical model,rdquo may also be of independent interest.

We consider the problem of determining from intrinsic properties whether or not a given spacelike surface is a Cauchy surface. We present three results relevant to this question. First, we derive necessary and sufficient conditions for a compact surface to be a Cauchy surface in a spacetime which admits one. Second, we show that for a non-compact surface it is impossible to determine whether or not it is a Cauchy surface without imposing some restriction on the entire spacetime. Third, we derive conditions for an asymptotically flat surface to be a Cauchy surface by imposing the global condition that it be imbedded in a weakly asymptotically simple and empty spacetime.