Note concerning gravitation and electromagnetism

The Maxwell equations for gravitational fields previously assumed by Sciama are derived from elementary considerations. The Lagrangian for a gravitating mass in a non-inertial coordinate system yields equations of motion leading to force definitions for a gravitational field intensity and a gravitational induction field. The non-inertial velocity of the coordinate system plays the role of a vector potential contributing to the generalized momenta of bodies moving in the system. A Lagrangian density constructed from the force-defined fields then lead to the source definitions of gravitational fields. It is found that positive field energy densities require repulsive gravitational forces, whereas attractive forces imply the violation of the conservation of energy. This paradox is resolved by representing gravitational quantities as pure-imaginary entities. Thus characterized, the equations which define gravitational fields become identical to Maxwell's equations but are pure-imaginary. This suggests a combined representation for gravitational and electromagnetic fields which, in covariant form, indicates both the well known equivalence of mass and energy and a possible equivalence of charge and energy. From orthogonality considerations, it is conjectured that this latter energy is gravitational, and that, whereas gravitational fields interact with electromagnetic energy, electromagnetic fields interact with gravitational energy. Parts of this work were completed at Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A.     

Production of massive spin — 1/2 particles in Robertson-Walker universes with external electromagnetic fields

In this paper we investigate the combined influence of both cosmological and electromagnetic particle creation mechanisms upon massive particles with spin 1/2 on the basis of general covariant Dirac theory.Curved space-time, a radiation-dominated Friedmann universe, is treated as an unquantized gravitational field and the low-frequency part of the 2.7 K background radiation is approximated by homogeneous, constant, and parallel external electric and magnetic fields. We calculate the number density of spin 1/2 particles with massm which are created under the influence of both these external fields.We find that the electric field and the magnetic field both amplify the genuine, purely gravitational particle production. This influence of the magnetic field, which is in contrast to its reducing effect as far as the creation of spin-zero particles is concerned, can clearly be traced back to its coupling to the spin of the particles.Under certain conditions the electromagnetic fields in the early universe can influence the particle creation process even more than the gravitational field.     

Gravitational lensing in quasar samples

The first cosmic mirage was discovered approximately 20 years ago as the double optical counterpart of a radio source. This phenomenon had been predicted some 70 years earlier as a consequence of General Relativity. We present here a summary of what we have learnt since. The applications are so numerous that we had to concentrate on a few selected aspects of this new field of research. This review is focused on strong gravitational lensing, i.e. the formation of multiple images, in QSO samples. It is intended to give the reader an up-to-date status of the observations and to present an overview of its most interesting potential applications in cosmology and astrophysics, as well as numerous important results achieved so far. The first section follows an intuitive approach to the basics of gravitational lensing and is developed in view of our interest in multiply imaged quasars. The astrophysical and cosmological applications of gravitational lensing are outlined in Sect. 2 and the most important results are presented in Sect. 5. Sections 3 and 4 are devoted to the observations. Finally, conclusions are summarized in the last section. We have tried to avoid duplication with existing (and excellent) introductions to the field of gravitational lensing. For this reason, we did not concentrate on the individual properties of specific lens models, as these are already well presented in Narayan and Bartelmann (1996) and on a more intuitive ground in Refsdal and Surdej (1994). Wambsganss (1998) proposes a broad view on gravitational lensing in astronomy; the reviews by Fort and Mellier (1994) and Hattori et al. (1999) deal with lensing by galaxy clusters; microlensing in the Galaxy and the local group is reviewed by Paczyński (1996) and a general panorama on weak lensing is given by Bartelmann and Schneider (1999) and Mellier (1999). The monograph on the theory of gravitational lensing by Schneider, Ehlers and Falco (1992) also remains a reference in the field. Received 4 April 2000 / Published online 9 August 2000     

Gravitational and electromagnetic emission by magnetized coalescing binary systems

We discuss the possibility to obtain an electromagnetic emission accompanying the gravitational waves emitted in the coalescence of a compact binary system. Motivated by the existence of black hole configurations with open magnetic field lines along the rotation axis, we consider a magnetic dipole in the system, the evolution of which leads to (i) electromagnetic radiation, and (ii) a contribution to the gravitational radiation, the luminosity of both being evaluated. Starting from the observations on magnetars, we impose upper limits for both the electromagnetic emission and the contribution of the magnetic dipole to the gravitational wave emission. Adopting this model for the evolution of neutron star binaries leading to short gamma ray bursts, we compare the correction originated by the electromagnetic field to the gravitational waves emission, finding that they are comparable for particular values of the magnetic field and of the orbital radius of the binary system. Finally we calculate the electromagnetic and gravitational wave energy outputs which result comparable for some values of magnetic field and radius.     

Propagation of light in a Maxwell-like gravitational field

We propose a coupling between the gravitational and electromagnetic fields so that we consider the electrodynamical Maxwell's equations as the basic ones and add the four-vector of gravitational potential to the differential operators occurring in it. It is shown that by means of this coupling all well-known tests of Einstein's theory of gravitation connected with the propagation of light in gravitational field can be correctly calculated.     

An axion-like scalar field environment effect on binary black hole merger

The environment, such as an accretion disk, could modify the signal of the gravitational wave from astrophysical black hole binaries. In this article, we model the matter field around intermediatemass binary black holes by means of an axion-like scalar field and investigate their joint evolution. In detail, we consider equal mass binary black holes surrounded by a shell of axion-like scalar field both in spherically symmetric and non-spherically symmetric cases, and with different strengths of the scalar field. Our result shows that the environmental scalar field could essentially modify the dynamics. Firstly,in the spherically symmetric case, with increase of the scalar field strength, the number of circular orbits for the binary black hole is reduced. This means that the scalar field could significantly accelerate the merger process. Secondly, once the scalar field strength exceeds a certain critical value, the scalar field could collapse into a third black hole with its mass being larger than that of the binary. Consequently,the new black hole that collapses from the environmental scalar field could accrete the binary promptly and the binary collides head-on with each other. In this process, there is almost no quadrupole signal produced, and, consequently, the gravitational wave is greatly suppressed. Thirdly, when the scalar field strength is relatively smaller than the critical value, the black hole orbit could develop eccentricity through accretion of the scalar field. Fourthly, during the initial stage of the inspiral, the gravitational attractive force from the axion-like scalar field could induce a sudden turn in the binary orbits, hence resulting in a transient wiggle in the gravitational waveform. Finally, in the non-spherical case, the scalar field could gravitationally attract the binary moving toward the center of mass for the scalar field and slow down the merger process.     

On a nonlinear and lorentz-invariant version of Newtonian gravitation — II

This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.     

引力波理论和实验的新进展

引力波的存在是爱因斯坦在广义相对论理论中提出的一个重要预言．由于目前技术水平的限制,无法在实验室产生足以被探测到的引力波,因此宇宙中大量的大质量剧烈活动的天体成为科学家研究引力波的首选,从而诞生了引力波天文学．引力波探测将开启研究宇宙的新窗口,是继电磁辐射、宇宙线和中微子探测后探索宇宙奥秘的又一重要手段,对天文学研究有着极为重要的意义.新一代应用了高灵敏度的迈克耳逊干涉仪装置的长基线引力波探测仪正在建造中．该综述从引力波理论出发,阐述了目前研究较多的可探测引力波源,给出了目前观测上的最新进展,并展望了今后的发展前景．     

Domain walls in Lyra geometry

In this paper we have discussed two models of domain walls within the framework of Lyra geometry. An exact solution is obtained for a thick non static domain wall. The space time is non singular both in its spatial and temporal behavior and the gravitational field experienced by a test particle is attractive. It is found that these exists no particle horizon in our case. Also we have presented a spherical domain wall with nonvanishing stress components in the direction perpendicular to the plane of the wall. The gravitational field of the domain wall is shown to be attractive in nature. This revised version was published online in July 2006 with corrections to the Cover Date.     

On gravitational radiation from binary systems

We discuss gravitational radiation from a neutral mass particle within a bound orbit in the background Schwarzschild metric. We compare the power loss of gravitational radiation according to this formalism with the heuristic quadrupole radiation formula as applied to a binary system. There are evidence and compelling reasons to believe that the quadrupole formula is valid even in a fairly strong gravitational field, although its fully consistent analytical derivation is not yet known. In particular, we emphasize that the application of the quadrupole formula to the binary pulsar system PSR 1913+16 as well as other binary pulsars, which are weakly bound by gravity, is well justified.     

Gravitational Field of Fractal Distribution of Particles

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss’s law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gravitational moments for fractal distribution are considered.     

Die Ausbreitung der skalaren Kugelwellen bis zur 2. Náherungsordnung im Gravitationsfeld mit Quadrupolstruktur

By means of the perturbation expansion scheme with respect to the gravitational constant we give a retarded solution of the covariant wave equation for the potential of a free massless scalar field in an axially symmetric gravitational background field of a point mass with a quadrupole moment. For the zeroth order solution we choose a spherical symmetric wave as an ansatz. Our results show that far from the source the spherical symmetric second order wave tail is effectively generated by the loss of mass, caused by gravitational radiation, and that all the other second order tail terms are compensable by first order multipole moments corresponding to a change of the boundary conditions.     

Effects of interplanetary dust on the LISA drag-free constellation

The analysis of non-radiative sources of static or time-dependent gravitational fields in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational effects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational field has been calculated for some ID density distributions that fit the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA Keplerian orbits around the Sun. This analysis can be eventually extended to Local Dark Matter (LDM), as gravitational fields are expected to be similar for ID and LDM distributions. Under some strong assumptions on the displacement noise at very low frequency, the Doppler data collected during the whole LISA mission could provide upper limits on ID and LDM densities.     

Physical background of the principle of equivalence

In this paper we assert that Einstein's assumption of the validity of special relativity in an infinitely small domain of space-time cannot be accepted if the dilatational degree of freedom exists as a natural key in explaining the existence of gravitation. In this case the equality of inertial and gravitational force holds through the whole structure of space-time but their intensities change continuously by following the behaviour of function which is responsible for reproduction of time and length units from point to point. In addition we discuss the way in which the pseudo-tensor of gravitational field was obtained.     

Convection in the mantle and its effect upon the earth's gravitational field

The failure of an equilibrium model to provide an adequate representation of the Earth's external gravitational field suggests that one should consider a more general hydrodynamical model for the interior of the terrestrial globe, and the most probable cause of motion, which may significantly effect the distribution of density inside the Earth, is convection throughout the mantle. In the present paper we investigate the effects of convection in the mantle on the gravitational field of the Earth and calculate the velocity of convection necessary to account for the observed characteristics of the external gravitational field.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Calculation of the perihelion advance of planets in a field approach to gravitation

It is shown that, when taking into account the self-gravity of field energy of a gravitational field, one obtains a modified field equation for the intensity of gravitational field, the solution of which, when inserted in Kepler's problem, furnishes a formula for the perihelion precession of planets which (except of a fitting numerical factor) is identical with Einstein's. In Appendix 1 we point out the significance of an analogous equation in electrodynamics, and in Appendix 2 we shall try to construct a field model within the relativistic field theory which justifies the previous perihelion-shift calculation.     

The Translational–Rotational Motion of an Earth Spheroid Satellite

In this paper we consider the translational–rotational motion of a spheroid satellite in the gravitational field, taking into account the asphericity of the earth. The harmonic coefficients of the earth’s gravitational field are taken up to J ₄. The equations of motion are obtained in terms of the canonical elements of Delaunay-Andoyer. A first order solution is obtained using the perturbing technique of Lie series.     

Magnetic deformation of magnetars for the giant flares of the soft gamma-ray repeaters

We present one possible mechanism for the giant flares of the soft gamma-ray repeaters (SGRs) within the framework of the magnetar (superstrongly magnetized neutron star) model, motivated by the positive period increase associated with the August 27 event from SGR 1900+14. From second-order perturbation analysis of the equilibrium of the magnetic polytrope, we find that there exist different equilibrium states separated by the energy of the giant flares and the shift in the moment of inertia to cause the period increase. This suggests that, if we assume that global reconfiguration of the internal magnetic field of     suddenly occurs, the positive period increase     as well as the energy ≳10⁴⁴ erg of the giant flares may be explained. The moment of inertia can increase with a release of energy, because the star shape deformed by the magnetic field can be prolate rather than oblate. In this mechanism, since oscillation of the neutron star will be excited, a ∼ ms-period pulsation of the burst profile and an emission of gravitational waves are expected. The gravitational waves could be detected by planned interferometers such as LIGO, VIRGO and LCGT.