Extrinsic Curvature and the Einstein Constraints

The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors which involves a weight function. In stationary spacetimes, there is a natural choice of the weight function such that the transverse traceless part of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex

Excision boundary conditions for black hole initial data

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference, minor content changes including additional post-Newtonian comparison. Version accepted by PR

Uniqueness and Non-uniqueness in the Einstein Constraints

The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of an elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte

Strongly Enhanced Hole-Phonon Coupling in the Metallic State of the Dilute Two-Dimensional Hole Gas

We have studied the temperature dependent phonon emission rate $P$($T$) of a strongly interacting ($r_s\geq$22) dilute 2D GaAs hole system using a standard carrier heating technique. In the still poorly understood metallic state, we observe that $P$($T$) changes from $P$($T$)$\sim T^5$ to $P$($T$)$\sim T^7$ above 100mK, indicating a crossover from screened piezoelectric(PZ) coupling to screened deformation potential(DP) coupling for hole-phonon scattering. Quantitative comparison with theory shows that the long range PZ coupling between holes and phonons has the expected magnitude; however, in the metallic state, the short range DP coupling between holes and phonons is {\it almost twenty times stronger} than expected from theory. The density dependence of $P$($T$) shows that it is {\it easier} to cool low density 2D holes in GaAs than higher density 2D hole systems.Comment: To appear in Phys. Rev. Let

Earth - venus trajectories, 1968-69, volume 4, part b

Earth-venus trajectories 1968-196

Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity

The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test. All of these tests are found to be stable, except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure

Initial data for Einstein's equations with superposed gravitational waves

A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with linear gravitational waves, and allows detailed control over characteristics of the superposed gravitational wave like shape, location and propagation direction. It is furthermore fully covariant with respect to spatial coordinate changes and allows for very large amplitude of the gravitational wave.Comment: Version accepted by PRD; added convergence plots, expanded discussion. 9 pages, 9 figure

Suppression of weak localization effects in low-density metallic 2D holes

We have measured the conductivity in a gated high-mobility GaAs two dimensional hole sample with densities in the range (7-17)x10^9 cm^-2 and at hole temperatures down to 5x10^-3 E_F. We measure the weak localization corrections to the conductivity g=G/(e^2/h) as a function of magnetic field (Delta g=0.019 +/- 0.006 at g=1.5 and T=9 mK) and temperature (d ln g/dT<0.0058 and 0.0084 at g=1.56 and 2.8). These values are less than a few percent of the value 1/pi predicted by standard weak localization theory for a disordered 2D Fermi liqui