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.     

Exact two-soliton solutions to the Einstein gravitational field equations

Following our previous work on the existence of 1-soliton solution to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field, we have found six sets of analytical 2-soliton solutions to the Einstein field equations under a certain ansatz in the absence of the stated background field. Numerical analysis shows that if the two solitons of the transverse nature are injected at space variable z±, the longitudinal field componentg ₃₃ will acquire non-zero values for a bounded spatial region at later time. The nature of the solitons becomes rather complex when they interact. The amplitudeg of each soliton may change its magnitude resulting from the interaction. We have found that we might interpret the evolution of one field component as the gravitational instanton in our solutions. We must remark also that the total energy of the interacting solitons remains constant, as expected, at all time. These solutions correspond to the situation where the Riemann tensor is in general non-zero and are truly non-trivial solutions.     

Detection of gravitational waves from astrophysical sources

Modern ground-based gravitational-wave antennas designed to detect bursts of gravitational radiation from astrophysical catastrophes are described. Basic antenna characteristics, peculiarities of the noise background in antennas from various sources, and methods of their suppression are presented. The contribution from cosmic rays to the background is estimated. New programs of searching for low-frequency gravitational waves and potentialities for increasing the sensitivity of antennas of new types are briefly described.     

On static spherical symmetric solutions of the Bach-Einstein gravitational field equations

For field equations of 4th order, follwing from a Lagrangian “Ricci scalar plus Weyl scalar”, it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = o nad r = ∞ resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme.     

Soliton solutions to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field

Using a differential geometry approach, we have found two sets of new solutions to Einstein's equation of gravity in the presence of a spherically-symmetrical gravitational background, like the Earth. The transverse and longitudinal components of the metric tensor representing the gravity waves are all soliton solutions, propagating towards the origin of the Earth. If we consider the situation where the static background field is absent, the solutions still remain soliton-like in nature. The difference between our result and Einstein's is attributed to the two approximations taken previously — weak field and harmonic condition.On study leave of absence from Zhong Shan University, China     

Biofluorescence and the extended red emission in astrophysical sources

A broad emission band over the wavelength range 6000–7500 Å in submicron dust in the galaxy and in M82 can be explained by fluorescence phenomena in low-temperature chloroplasts and bacterial pigments. Alternative explanations do not appear to be promising.     

Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations

The fourth order field equations proposed by TREDER with a linear combination of BACH 's tensor and EINSTEIN 's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry.     

Induced forces in the gravitational field

In this paper the expression for the magnitude of the so-called induced force, acting on a mass particle, is deduced. The origin of this force is causally connected to the increase of the rest mass of the particle in the gravitational field.     

The astrophysical consequences of the bimodal hydrodynamic solution of the super star cluster winds

The mass reinserted by young stars in an emerging massive compact cluster shows a bimodal hydrodynamic behaviour. In the inner parts of the cluster, it is thermally unstable, while in its outer parts it forms an outflowing wind. The chemical homogeneity/inhomogeneity of low/high-mass clusters demonstrates the relevance of this solution to the presence of single/multiple stellar populations. We show the consequences which the thermal instability of the reinserted mass has on galactic superwinds and discuss the open issues raised by the bimodal solution of stellar winds of massive clusters.     

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jean's criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.     

A model of the gravitational field of Amalthea

Utilizing the topographic model of Jovian moon Amalthea (Stooke, 1994) and supposing that its mass density is constant we derived its basic geometrical and dynamical characteristics. For calculations the harmonic model of topography of the degree and order 18 was selected. The model appears to fit the entire surface to a mean accuracy of a few hundred meters, except in the regions localized around longitudes 0° and 180°. On the basis of the harmonic expansion of the topography we estimated the volume (V = 2.43 ± 0.02 km³) and the mean radius of topographyr ₀ = (79.7 ± 0.2) km. Generalized moments of inertia up to the order 2, principal moments of inertia and orientation of the principal axes with respect to the original reference frame were also calculated. The results show that although Amalthea has extremely irregular shape it may be treated dynamically as an almost symmetric body (B C). Finally, the set of the Stokes coefficients up to the degree and order 9 was evaluated. The results are verified by direct numerical integration.     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.     

A note on the gravitational field of Phobos

Phobos' proximity to the Roche limit, and some of its consequences deserving attention by the Phobos' mission, are the subject of this note.     

The gravitational field of flat galaxies

A set of bi-orthogonal pairs of functions is derived which is especially suited for the calculation of the gravitational field of flat galaxies. The functions are Hankel tranforms of associated Laguerre functions, or Hankel-Laguerre functions. They can be calculated by means of recurrence relations, which are derived from a generating function.Numerical computations are most efficiently performed using a related set of Chebyshev type functions, which have more economic recurrence relations. The necessary algorithms for efficient calculation of the field are derived using the properties of Hankel-Laguerre functions.This field calculation, can be used for a relatively cheap and simple computer simulation of galaxies.     

The gravitational field of three-dimensional galaxies

The simplest method of calculating gravitational fields is to use a set of biorthogonal pairs of mass-potential functions. A suitable set of functions for three dimensional mass distributions is derived which uses ultraspherical polynomials. Algorithms for computing the gravitational field are discussed which attempt to maximise computational efficiency.     

The gravitational field of a disk

This note gives the gravitational potential of the disk {(x, y, z):x ² +y ² p ² , z=0} and the gravitational field at the point (x, y, z). Formulas for a ring can be obtained as the difference of our results for two different values ofp. Results are obtained in terms of elliptic integrals and we indicate how these functions can be computed efficiently. Formulas necessary for the computation of partial derivatives are also given.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration.     

Some secondary indications of gravitational collapse

A stellar core becomes somewhat less massive due to neutrinos radiated away during its collapse in a neutron star or a black hole. The paper deals with the hydrodynamic motion of stellar envelope induced by such a mass loss. Depending on the structure of the outer stellar layers, the motion results either in ejection of an envelope with mass and energy proper for Nova outbursts; or nearly instantaneous excitation of strong pulsations of the star; or lastly in a slow slipping away of the whole stellar envelope. These phenomena are of importance when more powerful events, like supernova outbursts presumably associated with gravitational collapse, are absent. Such secondary indications of gravitational collapse are of special interest, since they may be a single observable manifestation (besides neutrinos and gravitational waves) of massive black hole formation.