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

High power coupled CO2 waveguide laser array

A hollow-bore ridge waveguide technique for phase locking arrays of coupled CO2 rf excited waveguide lasers was demonstrated. Stable phase-locked operation of two- and three-channel arrays has been demonstrated at the 50 W output level. Preliminary experiments with a five-element array generated an output power of 95 W but phase-locked operation was not conclusively demonstrated

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach

We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for identical background data in the extended conformal thin-sandwich decomposition. We show that the Hamiltonian constraint alone, when expressed in a certain way, admits two branches of solutions with properties very similar to those found by Pfeiffer and York. We construct these two branches analytically for a constant-density star in spherical symmetry, but argue that this behavior is more general. In the case of the Hamiltonian constraint this non-uniqueness is well known to be related to the sign of one particular term, and we argue that the extended conformal thin-sandwich equations contain a similar term that causes the breakdown of uniqueness.Comment: 9 pages, 1 figur

Evaluation of positive G sub Z tolerance following simulated weightlessness (bedrest)

The magnitude of physiologic changes which are known to occur in human subjects exposed to varying levels of + G sub Z acceleration following bed rest simulation of weightlessness was studied. Bed rest effects were documented by fluid and electrolyte balance studies, maximal exercise capability, 70 deg passive tilt and lower body negative pressure tests and the ability to endure randomly prescribed acceleration profiles of +2G sub Z, +3G sub Z, and +4G sub Z. Six healthy male volunteers were studied during two weeks of bed rest after adequate control observations, followed by two weeks of recovery, followed by a second two-week period of bed rest at which time an Air Force cutaway anti-G suit was used to determine its effectiveness as a countermeasure for observed cardiovascular changes during acceleration. Results showed uniform and significant changes in all measured parameters as a consequence of bed rest including a reduced ability to tolerate +G sub Z acceleration. The use of anti-G suits significantly improved subject tolerance to all G exposures and returned measured parameters such as heart rate and blood pressure towards or to pre-bed-rest (control) values in four of the six cases

Osmotic pressure induced coupling between cooperativity and stability of a helix-coil transition

Most helix-coil transition theories can be characterized by a set of three parameters: energetic, describing the (free) energy cost of forming a helical state in one repeating unit; entropic, accounting for the decrease of entropy due to the helical state formation; and geometric, indicating how many repeating units are affected by the formation of one helical state. Depending on their effect on the helix-coil transition, solvents or co-solutes can be classified with respect to their action on these parameters. Solvent interactions that alter the entropic cost of helix formation by their osmotic action can affect both the stability (transition temperature) and the cooperativity (transition interval) of the helix-coil transition. A consistent inclusion of osmotic pressure effects in a description of helix-coil transition for poly(L-glutamic acid) in solution with polyethylene glycol can offer an explanation of the experimentally observed linear dependence of transition temperature on osmotic pressure as well as the concurrent changes in the cooperativity of the transition.Comment: 5 pages, 3 figures. To be submitted to Phys.Rev.Let

3+1 Approach to the Long Wavelength Iteration Scheme

Large-scale inhomogeneities and anisotropies are modeled using the Long Wavelength Iteration Scheme. In this scheme solutions are obtained as expansions in spatial gradients, which are taken to be small. It is shown that the choice of foliation for spacetime can make the iteration scheme more effective in two respects: (i) the shift vector can be chosen so as to dilute the effect of anisotropy on the late-time value of the extrinsic curvature of the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions present in a similar calculation using the synchronous gauge vanish when the spacelike hypersurfaces have extrinsic curvature with constant trace. We furthermore verify the main conclusion of the synchronous gauge calculation which is large-scale inhomogeneity decays if the matter--considered to be that of a perfect-fluid with a barotropic equation of state--violates the strong-energy condition. Finally, we obtain the solution for the lapse function and discuss its late-time behaviour. It is found that the lapse function is well-behaved when the matter violates the strong energy condition.Comment: 21 pages, TeX file, already publishe

On the existence of initial data containing isolated black holes

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX