计算光在引力场中偏折的新方法

利用光的量子论,能量守恒及弱等效原理得出电磁波传播在几何近似下,光线在引力场中的偏转角和波矢的关系. 利用引力场中电磁波方程,在弱场近似下给出了一般的计算光线偏转角度的方法. 具体计算了Schwarzchild引力场中光线的偏折及Kerr-Newman引力场中光线的偏折. 关键词： 引力场 电磁波方程 能量守恒 弱场近似     

Equivalence Principle and Radiation by a Uniformly Accelerated Charge

We address the old question of whether or not a uniformly accelerated charged particle radiates, and consequently, if weak equivalence principle is violated by electrodynamics. We show that radiation has different meanings; some absolute, some relative. Detecting photons or electromagnetic waves is not absolute, it depends both on the electromagnetic field and on the state of motion of the antenna. An antenna used by a Rindler observer does not detect any radiation from a uniformly accelerated co-moving charged particle. Therefore, a Rindler observer cannot decide whether or not he is in an accelerated lab or in a gravitational field. We also discuss the general case.     

A New Interpretation of MOND Based on Mach Principle and Generalized Equivalence Principle

A new interpretation is introduced for MOND based on the Sciama’s interpretation of Mach principle and an Unruh like effect, in the context of a generalized equivalence principle. It is argued that in a locally accelerated frame with acceleration a the appearance of a Rindler horizon may give rise to a constant acceleration a ₀ as the local properties of cosmological horizon or Hubble length. The total gravitational acceleration inside this frame becomes the combination of a with a ₀. For a≫a ₀, the conventional gravitational mass m _g interacts with the dominant acceleration as m _g a and application of Sciama’s interpretation leads to the standard Newtonian dynamics. For a≪a ₀, however, a reduced gravitational mass [`(m)]<sub>g</sub>\bar{m}_{g} interacts with the dominant acceleration as [`(m)]_ga₀\bar{m}_{g}a_{0} and the application of Sciama’s interpretation on this reduced gravitational mass leads to MOND. This introduces a third proposal for MOND: The modification of gravitational mass.     

Collapse and rebound of a charged dust-like star

It is shown that a charged spherically symmetric star, made out of a continuous superposition of thin shells with Poincaré stresses, undergoes gravitational collapse in free fall like an uncharged star of dust. The interior solution is a Friedmann universe matching the Reissner-Nordström geometry at the boundary of the star. When the absolute value of the chargeQ does not exceed the massM, the star rebounds elastically inside the event horizon at the radial coordinateQ ²/(2M). The further history of the charged star after the bounce is analyzed. Besides, a simple mechanism which accounts for the development of Poincaré stresses in an originally charged star of dust is suggested. It is also verified that the energy density is nonnegative all along the collapse process.     

Equivalence principle and electromagnetic field: no birefringence,no dilaton,and no axion

The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge “substratum” and the flux “substratum” are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the spacetime relation H = H(F) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F, is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.     

Dyon black hole and its mass formula in the Tomimatsu-Sato-Yamazaki space-time

It is shown that a dyon solution, characterized by five parameters (massM, angular momentumJ, electric chargeQ, magnetic charge Φ, and distortion parameter δ), has an event horizon for arbitrary odd integer δ and satisfies the Christodoulou-Ruffini mass formula.     

Constraints on unified theories from the experimental tests of the equivalence principle

The predictions of a general unified theory for the gravitational, electromagnetic and scalar field are compared with the results of the experimental tests of the equivalence principle. It is shown that the theoretical predictions do not disagree with experimental data provided that the coupling of the scalar to the electromagnetic field is suppressed by a factork 10^–3, or, alternatively, the scalar field is massive; in this case, a lower limit for its mass is obtained.     

Space-Time Fluctuations Induced by D-Branes and Their Effects on Neutrino Oscillations

Neutrino oscillations are analyzed in the Ellis-Mavromatos-Nanopoulos-Volkov (ENMV) model, where the quantum gravitational fluctuations of the space-time background are described by virtual D branes. Such fluctuations may induce neutrino oscillations if a violation of the equivalence principle or a tiny violation of the Lorentz invariance is imposed. In this framework, the oscillation length of neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the energy which is the scale characterizing the topological fluctuations in the vacuum.     

LETTER: Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce the neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is required. In this approach, the oscillation length of massless neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.     

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 field=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 _v =g _v –n _v . 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.     

Central limit theorems for the one-dimensional Rayleigh gas with semipermeable barriers

A version of the one-dimensional Rayleigh gas is considered: a point particle of massM (molecule), confined to the unit interval [0,1], is surrounded by an infinite ideal gas of point particles of mass 1 (atoms). The molecule interacts with the atoms and with the walls via elastic collision. Central limit theorems are proved for a wide class of additive functionals of this system (e.g. the number of collisions with the walls and the total length of the molecular path).Research partially supported by the Hungarian National Foundation for Scientific Research, grant No. 819/1     

On limiting field strengths in gravitation

We consider through the equivalence principle the existence of maximal and minimal field strengths in gravitation. We explore the consequences for gravitational collapse and for explaining the rotation curve of galaxies without invoking dark matter. Other interesting implications like maximal size of planetary systems are outlined.1. Note that, in our case, such results, both for electromagnetic and gravitational fields, are obtained when torsion is considered [8]: In fact, we have arrived at a minimum radius, for instance, of the electron, starting explicitly frm a modified Poisson's equation when a term containing the spin is incorporated through torsion.     

On the Gravitational Collapse in Relativistic Theories of Gravitation

Following Einstein, we consider a simple model of a star, namely a spherically symmetric distribution of particles which are all moving along circular orbits around the center of the particle cluster. According to arguments given by Einstein, Laue, Treder and others, the existence of stationary circular motions for all values of r can be considered as a necessary condition for all collapse-free relativistic (classical) theory o gravitation. The discussion shows that, assuming the validity of the weak principle of equivalence and the principle of causality, one has to consider theories with a g₀₀-function different from the Einstein-Schwarzschild one. We discuss some g₀₀ types and show that our point of view leads in the direction of gravitational equations with a cut-off length.     

The dual curvature tensors and dynamics of gravitomagnetic matter

Gravitomagnetic charge that can also be referred to as the dual mass or magnetic mass is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low‐motion weak‐field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the duality relationship in the dynamical theories between the gravitomagnetic charge (dual mass) and the gravitoelectric charge (mass) is also taken into account in the present paper.     

On Pointwise Decay of Linear Waves on a Schwarzschild Black Hole Background

We prove sharp pointwise t ⁻³ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates t ⁻⁴, and t ⁻⁶, respectively. We proceed by decomposition into angular momentum ℓ and summation of the decay estimates on the Regge-Wheeler equation for fixed ℓ. We encounter a dichotomy: the decay law in time is entirely determined by the asymptotic behavior of the Regge-Wheeler potential in the far field, whereas the growth of the constants in ℓ is dictated by the behavior of the Regge-Wheeler potential in a small neighborhood around its maximum. In other words, the tails are controlled by small energies, whereas the number of angular derivatives needed on the data is determined by energies close to the top of the Regge-Wheeler potential. This dichotomy corresponds to the well-known principle that for initial times the decay reflects the presence of complex resonances generated by the potential maximum, whereas for later times the tails are determined by the far field. However, we do not invoke complex resonances at all, but rely instead on semiclassical Sigal-Soffer type propagation estimates based on a Mourre bound near the top energy.     

Fractionally charged non-leaking dyons and fermions in a bag

We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2iα). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity. We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.     

Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier

We consider a multidimensional system consisting of a particle of massM and radiusr (molecule), surrounded by an infinite ideal gas of point particles of massm (atoms). The molecule is confined to the unit ball and interacts with its boundary (barrier) via elastic collision, while the atoms are not affected by the boundary. We obtain convergence to equilibrium for the molecule from almost every initial distribution on its position and velocity. Furthermore, we prove that the infinite composite system of the molecule and the atoms is Bernoulli.     

A new spin test for the equivalence principle

The existing impressive tests for the strong equivalence principle are reviewed and their classical nature is emphasized. The possibility is raised here that intrinsic quantum spins may behave differently from orbital angular momentum in gravitational fields. The techniques developed to measure the electric dipole moment of the neutron are shown to offer hopes of testing this hypothesis. Einstein's theory predicts a null result for this experiment. This would constitute the first quantum test for the strong equivalence principle. Deviation from a null result would invalidate Einstein's theory of gravitation, as well as indicate the failure of the discrete symmetries (P, T) in gravitation.This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.     

Interacting New Agegraphic Viscous Dark Energy with Varying <Emphasis Type="Italic">G</Emphasis>

We consider the new agegraphic model of dark energy with a varying gravitational constant, G, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.