High Sensitivity Torsion Balance Tests for LISA Proof Mass Modeling

We have built a highly sensitive torsion balance to investigate small forces between closely spaced gold coated surfaces. Such forces will occur between the LISA proof mass and its housing. These forces are not well understood and experimental investigations are imperative. We describe our torsion balance and present the noise of the system. A significant contribution to the LISA noise budget at low frequencies is the fluctuation in the surface potential difference between the proof mass and its housing. We present first results of these measurements with our apparatus.Comment: 6th International LISA Symposiu

Test of the Equivalence Principle Using a Rotating Torsion Balance

We used a continuously rotating torsion balance instrument to measure the acceleration difference of beryllium and titanium test bodies towards sources at a variety of distances. Our result Delta a=(0.6+/-3.1)x10^-15 m/s^2 improves limits on equivalence-principle violations with ranges from 1 m to infinity by an order of magnitude. The Eoetvoes parameter is eta=(0.3+/-1.8)x10^-13. By analyzing our data for accelerations towards the center of the Milky Way we find equal attractions of Be and Ti towards galactic dark matter, yielding eta=(-4 +/- 7)x10^-5. Space-fixed differential accelerations in any direction are limited to less than 8.8x10^-15 m/s^2 with 95% confidence.Comment: 4 pages, 4 figures; accepted for publication in PR

Late Time Tail of Wave Propagation on Curved Spacetime

The late time behavior of waves propagating on a general curved spacetime is studied. The late time tail is not necessarily an inverse power of time. Our work extends, places in context, and provides understanding for the known results for the Schwarzschild spacetime. Analytic and numerical results are in excellent agreement.Comment: 11 pages, WUGRAV-94-1

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure

Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 micrometers, probing distances less than the dark-energy length scale $\lambda_{\rm d}=\sqrt[4]{\hbar c/\rho_{\rm d}}\approx 85 \mu$m. We find with 95% confidence that the inverse-square law holds ($|\alpha| \leq 1$) down to a length scale $\lambda = 56 \mu$m and that an extra dimension must have a size $R \leq 44 \mu$m.Comment: 4 pages, 6 figure

Universality of massive scalar field late-time tails in black-hole spacetimes

The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by $\psi(t)\sim t^{-5/6}\sin [\omega (t)\times t]$, where $\omega(t)$ depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of -5/6 depends on neither the multipole mode $\ell$ nor on the spin rate of the black hole $a/M$. In all black hole spacetimes, massive scalar fields have the same late-time behavior irrespective of their initial data (i.e., angular distribution). Their late-time behavior is universal.Comment: 11 pages, 14 figures, published versio

Testing numerical relativity with the shifted gauge wave

Computational methods are essential to provide waveforms from coalescing black holes, which are expected to produce strong signals for the gravitational wave observatories being developed. Although partial simulations of the coalescence have been reported, scientifically useful waveforms have so far not been delivered. The goal of the AppleswithApples (AwA) Alliance is to design, coordinate and document standardized code tests for comparing numerical relativity codes. The first round of AwA tests have now being completed and the results are being analyzed. These initial tests are based upon periodic boundary conditions designed to isolate performance of the main evolution code. Here we describe and carry out an additional test with periodic boundary conditions which deals with an essential feature of the black hole excision problem, namely a non-vanishing shift. The test is a shifted version of the existing AwA gauge wave test. We show how a shift introduces an exponentially growing instability which violates the constraints of a standard harmonic formulation of Einstein's equations. We analyze the Cauchy problem in a harmonic gauge and discuss particular options for suppressing instabilities in the gauge wave tests. We implement these techniques in a finite difference evolution algorithm and present test results. Although our application here is limited to a model problem, the techniques should benefit the simulation of black holes using harmonic evolution codes.Comment: Submitted to special numerical relativity issue of Classical and Quantum Gravit

Analytical solutions for black-hole critical behaviour

Dynamical Einstein cluster is a spherical self-gravitating system of counterrotating particles, which may expand, oscillate and collapse. This system exhibits critical behaviour in its collapse at the threshold of black hole formation. It appears when the specific angular momentum of particles is tuned finely to the critical value. We find the unique exact self-similar solution at the threshold. This solution begins with a regular surface, involves timelike naked singularity formation and asymptotically approaches a static self-similar cluster.Comment: 4 pages, 3 figures, accepted for publication in General Relativity and Gravitation, typos correcte

Vacuum induced torque between corrugated metallic plates

We study the torque arising between two corrugated metallic plates due to the interaction with electromagnetic vacuum. This Casimir torque can be measured with torsion pendulum techniques for separation distances as large as 1$\mu$m. It allows one to probe the nontrivial geometry dependence of the Casimir energy in a configuration which can be evaluated theoretically with accuracy. In the optimal experimental configuration, the commonly used proximity force approximation turns out to overestimate the torque by a factor 2 or larger.Comment: 7 pages, 4 figures, to appear in Europhysics Letters. Technical problem with eps file for figure 4 was fixe