Hamiltonian formulation of the theory of interacting gravitational and electron fields

The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x^o = constant hyper-surfaces (“time gauge”) the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent.     

Non-linear quark theory of spin 2 fields (gravitational mesons). II

An equation for spin 1/2⁺ and 3/2⁺ fermions interacting with a 27-plet of gravitational mesons is derived by the confluence method in the framework of non-linear quark theory of elementary particles. The case of spin 1/2⁺ baryons is examined in detail, and the equation for the baryon octet is derived in the form of an equation for a spinor field in curved space (the Fok-Ivanenko equation). An effective metric is defined by means of the 27-plet of gravitational mesons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 7–11, April, 1973.     

On a possible unification of gravitational and weak interactions

Within the framework of Cartan's generalization of Einstein's theory of gravitation one can achieve a unification of gravitational and weak interactions by appropriate choice of the parameter that couples spin and torsion. The proposed spin-torsion coupling has negligible cosmic effects except at stages of evolution when 10⁸¹ nucleons are confined to a sphere with a radius of about one astronomical unit. For a single nuclear particle the gravitational effects of mass and spin balance at a radius of about 1% of its Compton wavelength, thus stabilizing it against gravitational collapse.This essay received the fourth award from the Gravity Research Foundation for 1975 (Editor).     

The effect of a gravitational induction force on the stellar orbits in galaxies

This paper explores the effect of a gravitational induction force, similar to gravito-electromagnetism but of several orders of magnitude larger, on a spiral galaxy. This would provide, because of the huge amount of mass currents associated with spirals, a rather large gravitational induction force. Standard gravitational dynamics is modified by adding an anti-symmetric force tensor analogous to electromagnetism. By choosing a special free space solution to the Einstein field equations, it was found that the resulting force field would drop off by an r ⁻¹ rather than an r ⁻² rule. Thus this new induction force would grow to dominance over the large distances associated with galaxies. Any r ⁻¹ force will produce the flat rotation curves that are observed in disk galaxies as well as explain the Tully-Fisher relationship. It would also explain why the inner core of the spirals remain Newtonian. Quite surprisingly, this simple hypothesis also seems to offer explanations for many other observed phenomena as well.     

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts(GRBs)trace the high-z universe,there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe.Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies.Assuming that all halos have the singular isothermal sphere(SIS)mass profile in the mass range 1010h?1M?M2×1013h?1M?and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample,we calculated the gravitational lensing probability in BATSE,Swift/BAT and Fermi/GBM GRBs,respectively.With an derived probability result in BATSE GRBs,we searched for lensed GRB pairs in the BATSE5B GRB Spectral catalog.The search did not find any convincing gravitationally lensed events.We discuss our result and future observations for GRB lensing observation.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Can quantum gravitational forces stop gravitational collapse?

We consider, in lowest order of the gravitational coupling constant G, the gravitational potential between two neutrons. As we have previously pointed out [1],the quantum (including spin) contributions to the gravitational field dominate for distances smaller than the Compton wavelength of the neutron. At such distances the gravitational force between two neutrons may be repulsive. In particular, the gravitational forces which are analogous to the familiar Darwin and Fermi forces of quantum electrodynamics are capable of stopping gravitational collapse. Our discussion is within the framework of Einstein's theory, but on a microscopic level. We conclude that gravitational collapse may be halted without the necessity of extending Einstein's theory à la Cartan or otherwise.     

A solution for galactic disks with Yukawian gravitational potential

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m _g) of this particle. For example, in order to obtain a galactic disk with a scale length of b∼ 10 kpc, we should have a massive graviton of m _g ≪ 10⁻⁵⁹g. This result is much more restrictive than those inferred from solar system observations.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

A constraint on the distance dependence of the gravitational constant

Extended supergravity theories predict the existence of vector and scalar bosons, besides the graviton, which in the static limit couple to the mass. An example is the graviphoton, leading to antigravity. If these bosons have a small mass (?10^?4 eV), an observable Yukawa term would be present in the gravitational potential in the newtonian limit. This can be parametrized by a distance dependent effective gravitational “constant” G(r). Defining G₀ = G(10 cm) and G_c = G(10³ km), the comparison between theory and observations of the white dwarf Sirius B results in $\text{G}{}_{\mathrm{<mtext>c</mtext>}}\text{G}{}_0\text{= 0.98 ± 0.08}$.     

The validity of the formulaE=mc 2 for gravitational energy

Theoretical evidence for the validity of the formulaE =mc ² for gravitational energy in general relativity is reviewed. For isolated bodies the formula applies to both the inertial mass and the mass as a source of gravity. The formula also holds for the case of the mass density (as a source of gravity) of an inhomogeneous medium with small-scale gravitational interactions.     

The gravitational spin-spin force

The gravitational spin-spin interaction between two rotating mass rings is derived in a very simple manner, by the use of an electromagnetic analogy. The feasibility of undertaking a gravitational spin-spin experiment in a laboratory is considered, and it is concluded that the effect is too small to be accurately determined.     

Interaction of gravitational waves with a superconducting cylindrical antenna

In this paper we investigate the effects of gravitational waves (GW) on a superconducting cylindrical antenna (S-antenna). We suggest that the electric fields induced by GW of dimensionless amplitudeh - 10^–24 in the interior of existing cylindrical antenna might be detectable.     

Weak equivalence principle and gauge theory of the tetrad gravitational field

The tetrad theory of gravitation corresponding to the Treder formulation of the weak equivalence principle is incompatible with the customary method for constructing a gauge theory for a tetrad gravitational field. In this formulation, the Lagrangian of the nongravitating mass is a direct covariant generalization of the partially relativistic expression to a Riemannian space-time V₄. This incompatibility is at odds with the resutt found in the tetrad formulation of the general theory of relativity derived from the requirement of localization of the Poincaré group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 18–21, April, 1978.     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

Toward improving the accuracy of testing the equivalence of the inertial and the gravitational mass under terrestrial conditions

An experiment aimed at testing the equivalence of the inertial and the gravitational mass is considered in which use is made of a facility including a vacuum chamber with two coupled oscillators (a pendulum and dynamical damper that form a vibrational system featuring two degrees of freedom) and falling onto the Sun. The layout of the facility and its basic parameters are presented. The pendulum and the dynamical damper have the same natural frequency, which is equal to the frequency of their rotation about the Sun. This frequency is dependent on the date of the experiment and can be calculated on the basis of the time equation. In the proposed facility, the amplitude of oscillations of the damper is 1.2×10^?5 rad, which is much greater than the value of 10^?7 rad previously achieved in the experiment that tested the equivalence principle to the highest precision of about 10^?12. This precision can be considerably improved. The result is presented that was obtained from a measurement during the solar eclipse in Moscow on August 11, 1999.     

Tests of gravitational theories using space probes

Several high-precision tests of gravitational theories applied to the field of a spherical mass particle (the Sun) are formulated and analyzed. These tests mainly involve the accurate timing by (on-board) atomic clocks of two-way radio signals between two spacecraft (transponders) in various solar orbits. Measures of the gravitational field to at least 1 part in 10⁸, or orderm/R, wherem is the Schwarzschild radius of the Sun andR is the astronomical unit, are aimed at, with an assumed round trip time precision of 10^–2 s or 1.5 m distance. Since it is important to distinguish between the radial coordinate parameters occurring in the theory of the tests and their common astronomical measurements based on classical assumptions, two of the tests include the means in principle of determining these coordinate parameters.     

Gravitational collapse of dissipative fluid as a source of gravitational waves

Gravitational collapse of cylindrical anisotropic fluid has been considered in analogy with the work of Misner and Sharp. Using Darmois matching conditions, the interior cylindrical dissipative fluid (in the form of shear viscosity and heat flux) is matched to an exterior vacuum Einstein–Rosen space–time. It is found that on the bounding 3-surface the radial pressure of the anisotropic perfect fluid is linearly related to the shear viscosity and the heat flux of the dissipative fluid on the boundary. This non-zero radial pressure on the bounding surface may be considered as the source of gravitational waves outside the collapsing matter distribution.     

Derivation of Treder-type gravitational equations from a variational principle

A single variation principle for the gravitational field and nongravitating matter leading to Treder-type gravitational equations is formulated. It is shown that when Treder's theory is modified in this manner the resulting special-relativistic theory of gravitation with 16-component gravitational potentials h _µ ⁽⁾ predicts 7/12 of the perihelion advance and 1/2 of the light deflection and light delay predicted by general relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–39, January, 1976.I thank Professor D. D. Ivanenko for a helpful discussion.