William A. Hiscock

Stability and causality in dissipative relativistic fluids

The standard theory of relativistic dissipative fluid mechanics developed by Eckart contains several undesirable features: thermal and viscous fluctuations propagate acausally; there exist generic short wavelength secular instabilities; and there is not a well posed initial value problem for rotating fluids. In this paper we examine whether the generalization of Eckarts theory developed by Israel has succeeded in eliminating these features. We first generalize Israels theory to include the possibility of nonuniform equilibrium configurations. This generalization allows us to describe equilibrium configurations which may be rotating and self-gravitating such as neutron stars. We then evaluate the stability conditions for these fluids and compute the characteristic velocities at which perturbations propagate. Our main result is that if these fluids are stable, then the characteristic velocities are subluminal and the perturbations propagate via hyperbolic equations. Thus Israels theory is causal for all stable fluids. In addition, there is no generic instability, and the initial value problem is well posed. In our opinion, for these reasons, Israels theory should replace Eckarts as the standard theory of relativistic dissipative fluid mechanics.

Sensitivity curves for spaceborne gravitational wave interferometers

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted ~after averaging over source position and polarization! by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first ~mostly! analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. PACS number~s!: 04.80.Nn, 95.55.Ym Advances in modern technology have ushered in an era of large laser interferometers designed to be used in the detection of gravitational radiation, both on the ground and in space. Such projects include the Laser Interferometric Gravitational Wave Observatory ~LIGO! and VIRGO @1,2# ground-based interferometers, and the proposed Laser Interferometer Space Antenna ~LISA! and OMEGA @3,4# spacebased interferometers. As these detectors come on-line, a new branch of astronomy will be created and a radically new view of the Universe is expected to be revealed. With the era of gravitational wave astronomy on the horizon, much effort has been devoted to the problem of categorizing sources of gravitational radiation, and extensive studies are underway to determine what sources will be visible to the various detectors. Typically, the sensitivity of detectors to sources of gravitational radiation has been illustrated using graphs which compare source strengths ~dimensionless strain! to instrument noise as functions of the gravitational wave frequency. Many different types of plots have appeared in the literature, ranging from single plots of spectral density to separate am

Nonlinear pathologies in relativistic heat-conducting fluid theories

Abstract Hyperbolicity and stability are analyzed in the nonlinear regimes of two theories of relativistic heat-conducting fluids. Both theories are found to be unstable and non-hyperbolic for sufficiently large deviations from equilibrium. One of these theories (an extended hydrodynamic theory) is well behaved for small (but finite) deviations from equilibrium.

Semiclassical gravitational effects near cosmic strings

Abstract The vacuum expectation value of the stress-energy tensor of an arbitrary collection of conformal massless free quantum fields (scalar, spinor, and vector) in the presence of a static, cylindrically symmetric cosmic string is found, up to an undetermined numerical constant. This quantum stress-energy tensor is then used as a source in the linearized semiclassical Einstein equations, which are solved to find the first-order (in Ł) corrections to the exterior metric of a static, cylindrically symmetric cosmic string. The main result is that, at first-order in Ł, the ( r , o) two-space is no longer a simple flat cone; to this order the ( r , o) two- space is a (linearized) hyperboloid, which asymptotically approaches the classical conical surface at large values of r . The asymptotic value of the deficit angle of the cone is unchanged, still being precisely 8 πμ .

LISA, binary stars, and the mass of the graviton

We extend and improve earlier estimates of the ability of the proposed LISA (Laser Interferometer Space Antenna) gravitational wave detector to place upper bounds on the graviton mass, m_g, by comparing the arrival times of gravitational and electromagnetic signals from binary star systems. We show that the best possible limit on m_g obtainable this way is ~ 50 times better than the current limit set by Solar System measurements. Among currently known, well-understood binaries, 4U1820-30 is the best for this purpose; LISA observations of 4U1820-30 should yield a limit ~ 3-4 times better than the present Solar System bound. AM CVn-type binaries offer the prospect of improving the limit by a factor of 10, if such systems can be better understood by the time of the LISA mission. We briefly discuss the likelihood that radio and optical searches during the next decade will yield binaries that more closely approach the best possible case.

Using binary stars to bound the mass of the graviton

Center for Backyard Astrophysics ~CBA!, 1 and are expected to be strong sources of monochromatic gravitational waves which should be easily visible to an instrument such as LISA with only a few minutes of signal integration. Simultaneous optical and gravitational wave observations will be useful in refining the current physical models used to describe these systems, and for testing relativistic theories of gravity in the radiative regime by comparing the propagation speeds of electromagnetic and gravitational wave signals. This paper examines how the comparison of the phase of the orbitally modulated electromagnetic signal ~the light curve! and a gravitational wave signal from an IBWD star system can be used to bound the mass of the graviton. If the mass of the graviton is assumed to be known by other measurements, then the observations may be used to determine the properties of the binary star system being monitored. Current conservative bounds on the graviton mass come from looking for violations of Newtonian gravity in surveys of planetary motions in the solar system. If gravity were described by a massive field, the Newtonian potential would have Yukawa modifications of the form V~ r!52 M r exp~2r/l g! ~1!

Stability of rotating stellar models in general relativity theory

We investigate the effects of viscosity and thermal conductivity on the stability of rotating stellar models in general relativity theory. The equations of motion for the perturbed fluid stellar model (including nonadiabatic and dissipative effects) are used to construct an energy functional for the perturbed motion of the star. This energy is used to investigate the stability of rotating stellar models. The most interesting results of our investigation are (1) that the generic gravitational radiation-induced secular instability (discovered by J. L. Friedman in rotating perfect fluid stars) does not exist in slowly rotating stars having nonzero dissipation coefficients; and (2) three conditions necessary for the stability of these models are (a) the Schwarzschild criterion, (b) subluminal sound velocity, and (c) the dissipation coefficients not being too large.

Unequal arm space-borne gravitational wave detectors

Unlike ground-based interferometric gravitational wave detectors, large space-based systems will not be rigid structures. When the end stations of the laser interferometer are freely flying spacecraft, the armlengths will change due to variations in the spacecraft positions along their orbital trajectories, so the precise equality of the arms that is required in a laboratory interferometer to cancel laser phase noise is not possible. However, using a method discovered by Tinto and Armstrong, a signal can be constructed in which laser phase noise exactly cancels out, even in an unequal arm interferometer. We examine the case where the ratio of the armlengths is a variable parameter, and compute the averaged gravitational wave transfer function as a function of that parameter. Example sensitivity curve calculations are presented for the expected design parameters of the proposed LISA interferometer, comparing it to a similar instrument with one arm shortened by a factor of 100, showing how the ratio of the armlengths will affect the overall sensitivity of the instrument.

Thermal divergences on the event horizons of two-dimensional black holes

The expectation value of the stress-energy tensor

Plane steady shock waves in Isreal-Stewart fluids

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