Nonsymmetric Gravitational Theory Research Articles

Spherical collapse of a nonrotating perfect fluid in the non-symmetric theory of gravitation

A set of time-dependent differential equations governing the behaviour of a spherically symmetric non-rotating perfect fluid in the non-symmetric theory of gravitation (NGT), is derived in a form suitable for numerical computations. This is then applied to the pressureless collapse of such a fluid. If the Newtonian potential does not exceed a certain value, and if the NGT potential is large enough, the collapse stops and reverses itself into an expansion before the Schwarzschild horizon is reached. A solution is presented for the case where the attractive tensor component of the NGT force is negligible. Bounds are found on the Newtonian potential and the ratio of NGT to Newtonian potentials within which the bounce phenomenon must occur.

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find “interference effects” between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar fieldρ=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing “mass without mass” and “charge without charge.” We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh μv =g μv −n μv . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the “gravitational constant”). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.

Generation via Limiting Procedures of New Solutions in a Nonsymmetric Gravitational Theory

New electromagnetic Bianchi type I solutious with nonzero cosmological constant, which satisfy the field equations of a nonsymmetric gravitational theory, are obtained from static solutions. This is achieved by taking a limit of the nonsymmetric tatic solutions.

Pulsar polarization measurements and the nonsymmetric gravitational theory.

Because of the breakdown of the Einstein equivalence principle in the nonsymmetric gravitational theory (NGT) of Moffat, orthogonally polarized electromagnetic waves can propagate at different velocities in a gravitational field. Moffat has proposed that galactic dark matter, in the form of cosmions, may act as a significant source of gravity in the NGT. We discuss how observations of the highly polarized radiation from distant pulsars could provide significant limits on the strength of the coupling of cosmions in the NGT.

Traversible wormholes and the negative-stress-energy problem in the nonsymmetric gravitational theory.

The stress-energy tensor for a a general spherically symmetric matter distribution in the nonsymmetric gravitational theory (NGT) is determined using a heuristic argument. Using this tensor and the NGT field equations, it is shown that a wormhole threaded with matter must necessarily have a radial tension greater than the mass-energy density in the throat region. Hence, as in general relativity, a traversible wormhole in NGT must contain matter with a negative stress energy.

Expansions of non-symmetric gravitational theories about a GR background

A large number of Lagrangian-based non-Riemannian geometrical theories of gravitation are consistently generated by the method of algebraic extension. Of this number, only two possess a physically viable excitation spectrum (particle content) when expanded about Minkowski spacetime. They are NGT (non-symmetric gravitational theory) and AHG (algebraically extended Hilbert gravity). The author undertakes the linear expansion of these two theories about an arbitrary vacuum general relativistic background spacetime. AHG fails to remain ghost free upon a non-flat background while NGT preserves its symmetries and particle content. NGT is the only AE Hermitean theory remaining in contention as an alternative theory to general relativity.

White dwarf and neutron star interior solutions in the nonsymmetric gravitational theory

Spherically symmetric, static, numerical solutions of the field equations of the nonsymmetric gravitational theory (NGT) for dense, homogeneous, cold matter with a stiff equation of state are presented in graphic form. As in Einstein's general relativity theory (GRT), two types of stable objects are predicted, corresponding to white dwarfs and neutron stars. The NGT makes these less stable as it effectively softens the equation of state, decreasing their mass and radius

Nonsymmetric gravitation theories and local Lorentz invariance.

We analyze the motion and internal structure of test bodies in theories of gravity which couple the antisymmetric part of a nonsymmetric-tensor gravitational field to the electromagnetic field. We establish that such theories necessarily violate the Einstein equivalence principle by breaking local Lorentz invariance. We also show how atomic-physics experiments designed to test the isotropy of space can be used to test these nonsymmetric theories of gravity. We comment briefly on the constraint such experiments are capable of imposing on Moffat's nonsymmetric gravitation theory, the prototype for the theories of gravity we study.

Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case

This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find “interference effects” between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh μν =g μν −η μν . We also deal with the Lagrangian for the scalar field (connected to the “gravitational constant”). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from “interference effects” in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.

Gravitational light deflection and propagation delay in nonsymmetric theories of gravity.

The gravitational deflection of light by the Sun and the closely related gravitational propagation delay are polarization dependent in any theory of gravity which couples the antisymmetric part of a nonsymmetric-tensor gravitational field to the electromagnetic field. This polarization dependence is a global consequence of the breakdown of the Einstein equivalence principle. The present version of Moffat's nonsymmetric gravitation theory, the prototype for the theories we study, predicts that light grazing the limb of the Sun is deflected by about a fifth of a milliarcsecond more when it is linearly polarized with its magnetic field lying in the plane in which the light is deflected than when it is orthogonally polarized. The next generation of light-deflection experiments will stringently test this prediction.

Testing the equivalence principle in the field of the Earth: Particle physics at masses below 1 microeV?

A sensitive, systematic search for feeble, macroscopic forces arising from the exchange of hypothetical ultra-low-mass bosons was made by observing the differential acceleration of two different test body pairs toward two different sources. Our differential accelerometer---a highly symmetric, continuously rotating torsion balance---incorporated several innovations that effectively suppressed systematic errors. All known sources of systematic error were demonstrated to be negligible in comparison to our fluctuating errors which are roughly 7 times larger than the fundamental limit set by the fact that we observe an oscillator at room temperature with a given damping time. Our $1\ensuremath{\sigma}$ limits on the horizontal differential acceleration of Be/Al or Be/Cu test body pairs in the field of the Earth, $\ensuremath{\Delta}{a}_{\ensuremath{\perp}}=(2.1\ifmmode\pm\else\textpm\fi{}2.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm ${\mathrm{s}}^{\ensuremath{-}2}$ and $\ensuremath{\Delta}{a}_{\ensuremath{\perp}}=(0.8\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm ${\mathrm{s}}^{\ensuremath{-}2}$, respectively, set improved bounds on Yukawa interactions mediated by bosons with masses ranging between ${m}_{b}{c}^{2}\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ and ${m}_{b}{c}^{2}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ eV. For example, our constraints on infinite-range vector interactions with charges of $B$ and of $B\ensuremath{-}L$ are roughly 10 and 2 times more sensitive than those obtained by Roll, Krotkov and Dicke using the field of the Sun. Furthermore we set stringent constraints down to $\ensuremath{\lambda}=1$ m, while those of solar experiments are weak for $\ensuremath{\lambda}<1$ AU. In terms of the weak equivalence principle in the field of the Earth, our $1\ensuremath{\sigma}$ result corresponds to $\frac{{m}_{i}}{{m}_{g}(\mathrm{Cu})}\ensuremath{-}\frac{{m}_{i}}{{m}_{g}(\mathrm{Be})}=(0.2\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$. Our results also yield stringent constraints on the nonsymmetric gravitation theory of Moffat and on the anomalous acceleration of antimatter in proposed "quantum gravity" models, and have implications for lunar-ranging tests of the strong equivalence principle. Our $1\ensuremath{\sigma}$ limit on the differential acceleration of Be/Al test body pairs toward a 1.5 Mg Pb laboratory source, $\ensuremath{\Delta}a=(\ensuremath{-}0.15\ifmmode\pm\else\textpm\fi{}1.31)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm ${\mathrm{s}}^{\ensuremath{-}2}$, provides constraints on Yukawa interactions with ranges down to 10 cm, and on interactions whose charge is $B\ensuremath{-}2L$.

Effects of the nonsymmetric gravitation theory and radial perturbations of the lunar orbit.

The predictions of the nonsymmetric gravitation theory of Moffat for the radial perturbations of the lunar orbit are computed. An effect is found but, given the accuracy of Lunar Laser Ranging Experiment data, it is not likely to be detected, even if the accuracy of the data is improved by a factor of 100. The calculation is done in a post-Newtonian coordinate frame. The transformation to an Earth-based normal coordinate frame is shown not to affect the results.

Spinning test particles and the motion of a gyroscope according to the nonsymmetric gravitation theory.

The motion of spinning test particles is derived in the nonsymmetric gravitation theory using the field equations of matter and the methods of Papapetrou. The predictions for the precession of a torque-free gyroscope in the gravitational field of the Earth, Jupiter, and the Sun are obtained and compared with the predictions of Einstein's gravitation theory.

The newly detected pulsar in SN 1987A as a test of gravitational theories

view Abstract Citations (2) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Newly Detected Pulsar in SN 1987A as a Test of Gravitational Theories Moffat, J. W. Abstract If the recently reported 0.5 ms period pulsed optical signal from SN 1987A is associated with a young neutron star, then a new important constraint on stable neutron star solutions of gravitational theories and the equations of state has been found. The very rapid pulsar period would imply that according to Einstein's gravitational theory (EGT), the neutron star is rotating with an angular velocity that is larger than the breakup angular velocity, which would cause an unrealistic constraint on the equation of state of nonexotic nuclear matter. It is shown that the break-up speed of a neutron star in the nonsymmetric gravitational theory (NGT) can be significantly larger than in EGT and allow for conventional realistic nuclear equations of state. Publication: The Astrophysical Journal Pub Date: December 1989 DOI: 10.1086/185607 Bibcode: 1989ApJ...347L..59M Keywords: Gravitation Theory; Neutron Stars; Pulsars; Supernova 1987a; Angular Velocity; Equations Of State; Stellar Rotation; Astrophysics; EQUATION OF STATE; GRAVITATION; PULSARS; STARS: NEUTRON; STARS: SUPERNOVAE full text sources ADS | data products SIMBAD (4) NED (2)

Detection of dark matter and tests of the weak equivalence principle.

Estimates of the predicted magnitude of deviations from Newtonian gravitation and the possible violations of the weak equivalence principle in the nonsymmetric gravitational theory (NGT), caused by cosmions in the earth, are given. An E\"otv\"os or free-fall Galileo experiment on the Earth's surface or in space with $\frac{\ensuremath{\Delta}a}{g}\ensuremath{\le}{10}^{\ensuremath{-}12}$ could test NGT and confirm the existence of dark matter.

Possible test at Jupiter of the nonsymmetric gravitational theory.

Radiometric data generated during spacecraft flybys of Jupiter have the capability to provide an interesting constraint on the coupling of cosmions in the nonsymmetric gravitational theory (NGT) of Moffat. It is shown that the close flyby of Jupiter by Pioneer 11 could imply a possible limit on the NGT $l$ parameter of the Sun of ${l}_{\ensuremath{\bigodot}}<2800$ km, a limit which could affect the ability of the NGT to account for the precession of the perihelion of Mercury with a large solar quadrupole moment.

The static spherically symmetric interior case of the non-symmetric theory of gravitation

The field equations for a spherically symmetric perfect fluid in non-symmetric gravitational theory are cast as a set of first-order differential equations suitable for numerical integration. An analytic series solution is presented as an expansion around r=0. It is shows how interior solutions match with the exterior one and how, at the boundary, the Euler equation for the fluid becomes the equation of motion of a test particle in the exterior metric. An expression is derived from a conserved pseudotensor for the total mass-energy of a static body in terms of its interior matter parameters.

Violation of the weak equivalence principle in theories of gravity with a nonsymmetric metric.

Theories of gravitation in which a nonsymmetric metric couples minimally to the electromagnetic field violate the weak equivalence principle (WEP) by predicting that test bodies with internal electrostatic energy fall with different accelerations. This further supports Schiff's conjecture that the WEP implies the Einstein equivalence principle whose consequence is that gravity is described by a symmetric spacetime metric. Constraints on the nonsymmetric gravitational theory of Moffat are placed using the results of a recent free-fall Galilean test of the WEP.

Cosmions in the nonsymmetric gravitational theory.

A phenomenological model is presented for the conserved fermion-number current in the nonsymmetric gravitational theory (NGT) based on the numbers of stable protons, neutrons, neutrinos, and cosmions (weakly interacting massive particles). By a suitable choice of the coupling constants, it is shown that the NGT is consistent with terrestrial observations and with the data for the solar system. A fit to the data of seven nondegenerate binary systems, including the data for DI Herculis and AS Cam, is given. The overall results are in accord with a solution of the problem of the cosmological missing dark matter. Agreement is also achieved with the data for the pulsar system PSR 1913 + 16 and the close cataclysmic binary system 4U 1820-30, involving gravitational radiation.

New ghost-free extensions of general relativity

The method of algebraic extension is shown to yield a large class of gravitational theories which are extensions of general relativity. Requiring positivity of energy in the flat-space limit of such theories provides some constraints, but a large set of theories of potential phenomenological interest survives this condition. Explicit examples of such theories include the non-symmetric gravitational theory of Moffat, algebraically extended Hilbert gravity and a one-parameter family of theories with dynamical torsion. In general such theories do not alter general relativistic post-Newtonian predictions for time delay experiments; rather they alter the non-linearities of the post-Newtonian gravitational potential. Such effects may be probed by measuring periastron shifts, as in the eclipsing binary systems Di Her and AS Cam, as well as in the binary pulsar PSR 1913+16.