Measurement of the Solar Gravitational Deflection of Radio Waves Using Very-Long-Baseline Interferometry

Topological steering of light by nematic vortices and analogy to cosmic strings

Liquid crystals are widely known for their technological uses in displays, electro-optics, photonics and nonlinear optics, but these applications typically rely on defining and switching non-topological spatial patterns of the optical axis. Here, we demonstrate how a liquid crystal's optical axis patterns with singular vortex lines can robustly steer beams of light. External stimuli, including an electric field and light itself, allow us to reconfigure these unusual light-matter interactions. Periodic arrays of vortices obtained by photo-patterning enable the vortex-mediated fission of optical solitons, yielding their lightning-like propagation patterns. Predesigned patterns and spatial trajectories of vortex lines in high-birefringence liquid crystals can steer light into closed loops or even knots. Our vortex lattices might find technological uses in beam steering, telecommunications, virtual reality implementations and anticounterfeiting, as well as possibly offering a model system for probing the interaction of light with defects, including the theoretically predicted, imagination-capturing light-steering action of cosmic strings, elusive defects in cosmology.

Probing Gravitational Waves from Pulsars in Brans–Dicke Theory

This paper comprises the theoretical background for the data analysis of gravitational waves (GWs) from spinning neutron stars in Brans–Dicke (BD) theory. Einstein’s general theory of relativity (GR) predicts only two tensor polarization states, but a generic metric theory of gravity can also possess scalar and vector polarization states. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third one is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Solar System tests of Hořava–Lifshitz gravity

In the present paper, we consider the possibility of observationally constraining Hořava gravity at the scale of the Solar System, by considering the classical tests of general relativity (perihelion precession of the planet Mercury, deflection of light by the Sun and the radar echo delay) for the spherically symmetric black hole Kehagias–Sfetsos solution of Hořava–Lifshitz gravity. All these gravitational effects can be fully explained in the framework of the vacuum solution of Hořava gravity. Moreover, the study of the classical general relativistic tests also constrains the free parameter of the solution. From the analysis of the perihelion precession of the planet Mercury, we obtain for the free parameter ω of the Kehagias–Sfetsos solution the constraint ω ≥3.212×10 −26  cm −2 , the deflection of light by the Sun gives ω ≥4.589×10 −26  cm −2 , while the radar echo delay observations can be explained if the value of ω satisfies the constraint ω ≥9.179×10 −26  cm −2 .

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Progress in lunar laser ranging tests of relativistic gravity

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the equivalence principle (EP); they also enable several very accurate tests of relativistic gravity. These analyses give an EP test of Delta(MG/MI)EP=(-1.0+/-1.4) x 10(-13). This result yields a strong equivalence principle (SEP) test of Delta(MG/MI)SEP=(-2.0+/-2.0) x 10(-13). Also, the corresponding SEP violation parameter eta is (4.4+/-4.5) x 10(-4), where eta=4beta-gamma-3 and both beta and gamma are post-Newtonian parameters. Using the Cassini gamma, the eta result yields beta-1=(1.2+/-1.1) x 10(-4). The geodetic precession test, expressed as a relative deviation from general relativity, is Kgp=-0.0019+/-0.0064. The search for a time variation in the gravitational constant results in G /G=(4+/-9) x 10(-13) yr(-1); consequently there is no evidence for local (approximately 1 AU) scale expansion of the solar system.

Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979-1999

We used very-long-baseline interferometry (VLBI) to measure the deflection by the Sun of radio waves emanating from distant compact radio sources. This bending is characterized in the parametrized post-Newtonian formalism by gamma, which is unity in general relativity. Using a large geodetic VLBI data set, we obtained gamma=0.9998(3)+/-0.0004(5) (estimated standard error). We found no systematic biases from our analysis of subgroups of data.

A test of general relativity using radio links with the Cassini spacecraft

According to general relativity, photons are deflected and delayed by the curvature of space-time produced by any mass. The bending and delay are proportional to gamma + 1, where the parameter gamma is unity in general relativity but zero in the newtonian model of gravity. The quantity gamma - 1 measures the degree to which gravity is not a purely geometric effect and is affected by other fields; such fields may have strongly influenced the early Universe, but would have now weakened so as to produce tiny--but still detectable--effects. Several experiments have confirmed to an accuracy of approximately 0.1% the predictions for the deflection and delay of photons produced by the Sun. Here we report a measurement of the frequency shift of radio photons to and from the Cassini spacecraft as they passed near the Sun. Our result, gamma = 1 + (2.1 +/- 2.3) x 10(-5), agrees with the predictions of standard general relativity with a sensitivity that approaches the level at which, theoretically, deviations are expected in some cosmological models.

Deflection of spacecraft trajectories as a new test of general relativity

We derive a simple formula which gives the general relativistic deflection of a spacecraft, idealized as a point mass, for all values of the asymptotic speed V(infinity) (0< or =V(infinity)< or =1). Using this formula we suggest a new test of general relativity (GR) which can be carried out during a proposed interstellar mission that involves a close pass of the Sun. We show that, with foreseeable improvements in spacecraft tracking sensitivity, the deflection of a spacecraft's trajectory in the gravitational field of the Sun could provide a new test of GR.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Gravitational Lensing in Astronomy

Deflection of light by gravity was predicted by General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically. Among them were: the possibility of multiple or ring-like images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility of determining Hubble's constant with lensing. It is only relatively recently, (after the discovery of the first doubly imaged quasar in 1979), that gravitational lensing has became an observational science. Today lensing is a booming part of astrophysics. In addition to multiply-imaged quasars, a number of other aspects of lensing have been discovered: For example, giant luminous arcs, quasar microlensing, Einstein rings, galactic microlensing events, arclets, and weak gravitational lensing. At present, literally hundreds of individual gravitational lens phenomena are known. Although still in its childhood, lensing has established itself as a very useful astrophysical tool with some remarkable successes. It has contributed significant new results in areas as different as the cosmological distance scale, the large scale matter distribution in the universe, mass and mass distribution of galaxy clusters, the physics of quasars, dark matter in galaxy halos, and galaxy structure. Looking at these successes in the recent past we predict an even more luminous future for gravitational lensing.

ELECTRONIC SUPPLEMENTARY MATERIAL

Supplementary material is available for this article at 10.12942/lrr-1998-12.