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NASA NTRS1991

Probing the Higgs vacuum with general relativity

It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.

Mannheim, Philip D.↗
NASA NTRS1975

General relativity and satellite orbits

The general relativistic correction to the position of a satellite is found by retaining Newtonian physics for an observer on the satellite and introducing a potential. The potential is expanded in terms of the Keplerian elements of the orbit and substituted in Lagrange's equations. Integration of the equations shows that a typical earth satellite with small orbital eccentricity is displaced by about 17 cm. from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. The moon is displaced by about the same amounts. Application of the equations to Mercury gives a total displacement of about 58 km. after one orbit and a maximum periodic displacement of about 12 km.

Rubincam, D. P.↗
NASA NTRS1983

Rastall's and related theories are conservative gravitational theories although physically inequivalent to general relativity

The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.

Smalley, L. L.↗
NASA NTRS1973

Time-delay test of general relativity and Earth-Mars ephemeris improvement from analysis of Mariner 9 tracking data

Because of the large systematic errors that accompany the conversion of spacecraft ranging data to equivalent Earth-Mars time delays, the corresponding determination of gamma does not now allow the predictions of general relativity to be distinguished from those of the Brans-Dicke scalar-tensor theory with the fraction s of scalar field admixture being 0.06. The uncertainty in the determination of (1 plus gamma)/2 at the present stage of the Mariner 9 data analysis is at about the 10% level. The ephemeris of Mars suffers from the same problem: Only with the elimination of a major fraction of the systematic errors affecting the Mariner 9 pseudo observables will a truly substantial improvement be possible in the determination of the orbit.

Shapiro, I. I.↗
NASA NTRS1975

Experimental test of general relativity using time-delay data from Mariner 6 and Mariner 7

Range and Doppler data from Mariner 6 and Mariner 7 have been analyzed for purposes of measuring the effect of the sun's gravity field on S-band radio transmissions to the spacecraft. The prediction of general relativity, that the round-trip time delays between the station and the spacecraft will be increased by about 200 microsec near superior conjunction, has been verified with an uncertainty of 3 per cent or less. The dominant error source on the experiment is the stochastic nongravitational forces which act on the spacecraft and which limit the accuracy of the determination of the Mariner orbits. Effects of free coronal electrons on the round-trip propagation also make the measurement difficult, but the coronal contribution to the error is only about 1 per cent. Separate analyses of data from Mariner 6 and Mariner 7 yield two values near unity for the parameter gamma* which differ by about 0.3 per cent from each other. This and other considerations suggest that the error in the experiment is perhaps less than 3 per cent.

Anderson, J. D.↗
NASA NTRS1992

Spin-up of a rapidly rotating star by angular momentum loss - Effects of general relativity

It has recently been shown that a rapidly rotating Newtonian star can spin up by radiating angular momentum. Extremely fast pulsars losing energy and angular momentum by magnetic dipole radiation or gravitational radiation may exhibit this behavior. Here, we show that this phenomenon is more widespread for rapidly rotating stars in general relativity. We construct and tabulate polytropic sequences of fully relativistic rotating stars of constant rest mass and entropy. We find that the range of adiabatic indices allowing spin-up extends somewhat above 4/3 because of the nonlinear effects of relativistic gravity. In addition, there is a new class of 'supramassive' stars which will inevitably spin up by losing angular momentum regardless of their equation of state. A supramassive star, spinning up via angular momentum loss, will ultimately evolve until it becomes unstable to catastrophic collapse to a black hole. Spin-up in a rapidly rotating star may thus be an observational precursor to such collapse.

Cook, Gregory B.↗
NASA NTRS1989

Testing general relativity with Landers on the Martian satellite Phobos

A planned experiment to obtain range and Doppler data with the Phobos 2 Lander on the surface of the Martian satellite Phobos is described. With the successful insertion on January 29, 1989 of Phobos 2 into Mars orbit, it is anticipated that the Lander will be placed on the surface of Phobos in April 1989. Depending on the longevity of the Lander, range and Doppler data for a period of from one to several years are expected. Because these data are of value in performing solar-system tests of general relativity, the current accuracy of the relevant relativity tests using Deep Space Network data from the Mariner-9 orbiter of Mars in 1971 and from the Viking Landers in 1976-1982 is reviewed. The expected improvement from data anticipated during the Phobos 2 Lander Mission is also discussed; most important will be an improved sensitivity to any time variation in the gravitational 'constant' as measured in atomic units.

Anderson, J. D.↗
NASA NTRS1985

The apsidal motion of the eccentric eclipsing binary DI Herculis - An apparent discrepancy with general relativity

The apsidal motion of the eccentric eclipsing binary DI Herculis (HD 175227) is determined from an analysis of the available observations and eclipse timings from 1959 to 1984. Least squares solutions to the primary and secondary minima extending over an 84-yr interval yielded a small advance of periastron omega dot of 0.65 deg/100 yr + or - 0.18/100 yr. The observed advance of the periastron is about one seventh of the theoretical value of 4.27 deg/100 yr that is expected from the combined relativistic and classical effects. The discrepancy is about -3.62 deg/100 yr, or a magnitude of about 20 sigma. Classical mechanisms which explain the discrepancy are discussed, together with the possibility that there may be problems with general relativity itself.

Guinan, E. F.↗
NASA NTRS1990

The effects of general relativity on near-earth satellites

Whether one uses a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of three years of laser tracking data taken on the Lageos satellite. It is demonstrated that the simpler formulation in the geocentric frame is adequate for the purpose of near-earth satellite orbit determination. A correction to the conventional barycentric equations of motion is shown to be required.

Ries, J. C.↗
NASA NTRS1988

Effect of general relativity on a near-Earth satellite in the geocentric and barycentric reference frames

Whether one uses a solar-system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determinations for near-Earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of real laser-tracking data. A correction to the conventional barycentric equations of motion is shown to be required.

Ries, J. C.↗
NASA NTRS1993

The problem of exact interior solutions for rotating rigid bodies in general relativity

The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.

Wahlquist, H. D.↗
NASA NTRS1986

Teleparallelism as a universal connection on null hypersurfaces in general relativity

It is shown that a close relationship between the inner geometry of a null hypersurface N3 and the Newman-Penrose (NP) (1962, 1963) spin coefficient formalism exists. Projecting the null complex NP tetrad onto N3, two triads of basis vectors in N3 are obtained. The inner geometry of N3 is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators of N3, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form of N3. The resulting generalized Gauss-Codazzi equations are identical to nine of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally a general proof of Penrose's theorem that the shear of the null generators of N3 is the only initial null datum for a gravitational field on N3 is presented.

Mazur, P. O.↗
DOE OSTI2024

Initial data for first-order causal viscous conformal fluids in general relativity

We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.

Disconzi, Marcelo (ORCID:0000000234497778)↗