Rigid motions in Einstein spaces

Rigid motion in Einstein space-time using dyadic formulation of general relativit

The implications of precise timekeeping of Doppler gravitational wave observations

Gravitational radiation from galactic and extragalactic astrophysical sources will induce spatial strains in the solar system, strains which can be measured directly by the Doppler radio link to distant spacecraft. Current noise sources in Pioneer and Voyager Doppler data are delineated and a comparison is made with expected signal levels from gravitational wave sources. The main conclusion is that it is possible to detect gravitational radiation with current DSN hydrogen maser systems stable in fractional frequency + or - 2 x 10 to the minus 14th power over 1000 sec. In the future, however, a serious Doppler observational program in gravitational wave astronomy will require frequency systems stable to at least 10 to the minus 16th power, but at the same time the current single frequency S-band uplink transmission will have to be replaced by a dual frequency capability

SyZyGy: A Straight Interferometric Spacecraft System for Gravity Wave Observations

We apply TDI, unfolding the general triangular configuration, to the special case of a linear array of three spacecraft. We show that such an array ("SyZyGy") has, compared with an equilateral triangle GW detector of the same scale, degraded (but non-zero) sensitivity at low-frequencies (f<<c/(arrany size)) but similar peak and high-frequency sensitivities to GWs. Sensitivity curves are presented for SyZyGys having various arm-lengths. A number of technical simplifications result from the linear configuration. These include only one faceted (e.g., cubical) proof mass per spacecraft, intra-spacecraft laser metrology needed only at the central spacecraft, placement in a single appropriate orbit can reduce Doppler drifts so that no laser beam modulation is required for ultra-stable oscillator noise calibration, and little or no time-dependent articulation of the telescopes to maintain pointing. Because SyZyGy's sensitivity falls off more sharply at low frequency than that of an equilateral triangular array, it may be more useful for GW observations in the band between those of ground-based interferometers (10-2000 Hz) and LISA (.1 mHz-.1 Hz). A SyZyGy with ~1 light- second scale could, for the same instrumental assumptions as LISA, make obseervations in this intermediate frequency GW band with 5 sigma sensitivity to sinusoidal waves of ~2.5 x 10^-23 in a year's integration.Comment: 13 pages, 6 figures; typos corrected, figure modified, references adde

Hyperbolic Equations for Vacuum Gravity Using Special Orthonormal Frames

By adopting Nester's higher dimensional special orthonormal frames (HSOF) the tetrad equations for vacuum gravity are put into first order symmetric hyperbolic (FOSH) form with constant coefficients, independent of any time slicing or coordinate specialization.Comment: 14 pages, 3 figures, LaTeX, 13 macros. CQG 14 (1997) 1237-1247 has algebraic errors. +/- signs in Equations (2), (4) and (5) are here corrected, and factors of 2 added to Eqs. (18) and (19

The Effects of Orbital Motion on LISA Time Delay Interferometry

In an effort to eliminate laser phase noise in laser interferometer spaceborne gravitational wave detectors, several combinations of signals have been found that allow the laser noise to be canceled out while gravitational wave signals remain. This process is called time delay interferometry (TDI). In the papers that defined the TDI variables, their performance was evaluated in the limit that the gravitational wave detector is fixed in space. However, the performance depends on certain symmetries in the armlengths that are available if the detector is fixed in space, but that will be broken in the actual rotating and flexing configuration produced by the LISA orbits. In this paper we investigate the performance of these TDI variables for the real LISA orbits. First, addressing the effects of rotation, we verify Daniel Shaddock's result that the Sagnac variables will not cancel out the laser phase noise, and we also find the same result for the symmetric Sagnac variable. The loss of the latter variable would be particularly unfortunate since this variable also cancels out gravitational wave signal, allowing instrument noise in the detector to be isolated and measured. Fortunately, we have found a set of more complicated TDI variables, which we call Delta-Sagnac variables, one of which accomplishes the same goal as the symmetric Sagnac variable to good accuracy. Finally, however, as we investigate the effects of the flexing of the detector arms due to non-circular orbital motion, we show that all variables, including the interferometer variables, which survive the rotation-induced loss of direction symmetry, will not completely cancel laser phase noise when the armlengths are changing with time. This unavoidable problem will place a stringent requirement on laser stability of 5 Hz per root Hz.Comment: 12 pages, 2 figure

RECOGNITION OF TAXONOMICALLY SIGNIFICANT CLUSTERS NEAR THE SPECIES LEVEL, USING COMPUTATIONALLY INTENSE METHODS, WITH EXAMPLES FROM THE STEPHANODISCUS NIAGARAE COMPLEX (BACILLARIOPHYCEAE) 1

Since the early 1960s, numerical techniques have produced a wide variety of methods to suggest classifications of organisms based on quantitative measurements. A long-recognized shortcoming of these methods is that they will suggest classifications for any group of organisms and any set of measurements, whether or not the clusters in the suggested classification have any natural meaning or significance. Some progress has been made in assessing the reality of clusters determined by various methods. Data simulated to reflect known cluster structure have been used to test the accuracy of different methods, Various methods have been applied to the same data sets to compare how well they realize various desirable properties. Here we define a data-based model of randomness to represent what might be meant by “no natural basis for subdivision into clusters” and use it to compare an observed measure of cluster distinctness to the distribution of this measure predicted by this model of randomness. In this way, unwarranted subdivision can be statistically avoided, and significant subdivisions can be investigated with confidence. Our methods are illustrated with some examples from the Stephanodiscus niagarae Ehrenb. species complex. Significant differences in morphologic expression are identified in S. reimerii Theriot and Stoermer in Theriot, S. superiorensis Theriot and Stoermer and S. yellowstonensis Theriot and Stoermer. In addition, statistically significant clusters are identified in S. niagarae populations from different geographic locations and in members of the same population grown in different environments. These results suggest current criteria for resolving diatom taxa may not be sufficient to discern subtle differences that occur between real species.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65691/1/j.0022-3646.1997.01049.x.pd

Conservation laws for vacuum tetrad gravity

Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.Comment: Final version with additional reference

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. We find that previous treatments of LISA have underestimated its sensitivity by a factor of $\sqrt{3}$.Comment: 27 pages + 5 figures, REVTeX, accepted for publication in Phys Rev D; Update reflects referees comments, figure 3 clarified, figure 5 corrected for LISA baselin

Character Analysis In The Banisteriopsis Campestris Complex (Malpighiaceae), Using Spatial Auto‐Correlation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149728/1/tax02450.pd

Significance of c/sqrt(2) in Relativistic Physics

In the description of \emph{relative} motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation can be simply illustrated in the case of motion in one dimension. For one-dimensional motion, such first-order accelerations are multiplied by $(1-V^2/V_c^2)$, where $V_c=c/\sqrt{2}$ is the critical speed. If the speed of relative motion exceeds $V_c$, there is a sign reversal with consequences that are contrary to Newtonian expectations.Comment: 7 pages, 1 figure, slightly expanded version accepted for publication in Class. Quantum Gra