Thin Domain Walls in Lyra Geometry

This paper studies thin domain walls within the frame work of Lyra Geometry. We have considered two models. First one is the thin domain wall with negligible pressures perpendicular and transverse direction to the wall and secondly, we take a particular type of thin domain wall where the pressure in the perpendicular direction is negligible but transverse pressures are existed. It is shown that the thin domain walls have no particle horizon and the gravitational force due to them is attractive.     

Gravitational field of domain wall in Lyra geometry

In this paper, we study the domain wall with time dependent displacement vectors based on Lyra geometry in normal gauge i.e. displacement vector φ _i ^* =[β(t),0,0,0]. The field theoretic energy momentum tensor is considered with zero pressure perpendicular to the wall. We find an exact solutions of Einstein’s equation for a scalar field φ with a potential V(φ) describing the gravitational field of a plane symmetric domain wall. We have seen that the hyper surfaces parallel to the wall (z=constant) are three dimensional de-sitter spaces. It is also shown that the gravitational field experienced by test particle is attractive.     

Higher dimensional thick domain wall in Lyra geometry

An exact solution is obtained for a thick domain wall in a five dimensional Kaluza-Klein space time within the framework of Lyra geometry. The space time is nonsingular both in its spatial and temporal behavior. It is shown that the domain wall has no particle horizon and the gravitational force due to them is attractive. This revised version was published online in July 2006 with corrections to the Cover Date.     

Vacuumless topological defects in Lyra geometry

Few years ago, Cho and Vilenkin have proposed that topological defects can arise in symmetry breaking models without having degenerate vacua. These types of defects are known as vacuumless defects. In the present work, the gravitational field of a vacuumless global string and global monopole have been investigated in the context of Lyra geometry. We find the metric of the vacuumless global string and global monopole in the weak field approximations. It has been shown that the vacuumless global string can have repulsive whereas global monopole exerts attractive gravitational effects on a test particle. It is dissimilar to the case studied in general relativity.     

Gravitational Field of Domain Walls in Higher Dimension

In this paper, we study the gravitational field of domain wall in fivedimensional space-time. Exact solutions of Einstein's equations for a scalarfield with a potential V(Ø) are presented, describing thegravitational field of plane symmetric domain walls. The solution showsthat the energy density as well as pressure in the perpendicular directionon both sides of the walls to be reflection symmetric with respect to thewalls.PACS numbers: 98.80 cq, 0450     

Relativistic gravitational potential and its relation to mass-energy

From the general theory of relativity a relation is deduced between the mass of a particle and the gravitational field at the position of the particle. For this purpose the fall of a particle of negligible mass in the gravitational field of a massive body is used. After establishing the relativistic potential and its relationship to the rest mass of the particle, we show, assuming conservation of mass-energy, that the difference between two potential-levels depends upon the value of the radial metric coefficient at the position of an observer. Further, it is proved that the relativistic potential is compatible with the general concept of the potential also from the standpoint of kinematics. In the third section it is shown that, although the mass-energy of a body is a function of the distance from it, this does not influence the relativistic potential of the body itself. From this conclusion it follows that the mass-energy of a particle in a gravitational field is anisotropic; isotropic is the mass only. Further, the possibility of an incidental feed-back between two masses is ruled out, and the law of the composition of the relativistic gravitational potentials is deduced. Finally, it is shown, by means of a simple model, that local inhomogeneities in the ideal fluid filling the Universe have negligible influence on the total potential in large regions.     

Multiwavelength focusing with the Sun as gravitational lens

The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at infinity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed.The perturbations by the solar corona plasma will significantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 10⁸ amplification factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single field. Some possible targets are considered, such as Sagitarius A observed in X and γ rays.In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericity of the sun and coronal plasma index, we derive limits within which such observations could be possible.     

Periodic Orbits Around a Massive Straight Segment

In this paper, we consider the motion of a particle under the gravitational field of a massive straight segment. This model is used as an approximation to the gravitational field of irregular shaped bodies, such as asteroids, comet nuclei and planets's moons. For this potential, we find several families of periodic orbits and bifurcations. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Local integrals and the plane motion of a point in rotating systems

This paper deals with the plane motion of a star in the gravitational field of a system which is in a steady state and rotates with a constant angular velocity. For these systems a class of potentials permitting a local integral, linear with respect to the velocity components, has been found. The concept of the local integral itself was introduced by one of the authors of the present paper (Antonov, 1981). A detailed model has been constructed. The corresponding domain of the particle motion and the form of the trajectory coils have been determined. The result is compared with the motion in a more realistic potential.     

Quantum gravitomagnetic clock effect in Kerr gravitational field

We have found an approximate solution of Dirac equation using Foldy-Wouthuysen-Tani Hamiltonian of a Dirac particle in the Kerr gravitational field. We have solved the equation approximately using time-independent perturbation theory for the positive energy states. We have found frequencies by which these states oscillate. Difference of the periods of any of these two states has an identical form of the classical gravitomagnetic clock effect where the terms are quantized. So that, we have found a quantum version of the gravitomagnetic clock effect of a Dirac fermion in the Kerr gravitational field.     

Gravitational instability of a Hall plasma in the presence of suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting selfgravitating gas particle medium in the presence of suspended particles of a Hall plasma is considered. The particular cases of the effects of Hall currents and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

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.     

On particle trajectories in restricted 3-body problem including the effect of radiation: Sun-Jupiter system

In this work, we have simulated orbits of a particle moving in gravitational field of the Sun-Jupiter system. The effect of solar radiation pressure, including Poynting Robertson drag, on the evolution of particle orbits in phase space have been studied for different values of the parameter β ₁ (the ratio of radiation to gravitational force) and initial conditions. Characteristics of various computed trajectories have been studied using wavelet transform (WT), Fourier transform (FT) and Poincare surface of section method. We use wavelet analysis to identify transitions of a trajectory in time-frequency plane and further apply it to classify it as regular or chaotic in phase space. Unlike the Fourier transform method (FT), we observe that the wavelet transform (WT) also provides a basis to identify ‘sticky’ trajectories in the present dynamical system.     

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.     

Velocity dispersion in particulate disks with size distribution

Quasi-equilibrium solutions for the pre-planetary disk are studied in terms of Hämeen-Anttila's theory (1984) of collisional, self-gravitating systems. The distribution of particle sizes is assumed to follow simple power-law distributions, with a power index in the range of 1.5–5.0. The treatment includes mutual impacts with a velocity dependent coefficient of restitution, as well as gravitational encounters with dynamical friction. The mean gravitational field of the disk is also taken into account. The results indicate that the energy(equi)-partition depends mainly on the index of size distribution, but is also affected by the optical thickness of the system, as well as on the vertical thickness as compared to the particle size. The vertical component of the gravitational field is found to be important, especially when the mass of the system is concentrated on the large particles.     

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.     

Cosmological models with time-varying gravitational and cosmological “constants”

The evolution and dynamics of a locally-rotationally-symmetric (LRS) Bianchi type-V space-time cosmological models are discussed with variable gravitational and cosmological “constants” in context of the particle creation. We present the exact solutions of Einstein field equations by using a power-law form of the average scale factor of the metric in the case of the particle creation and in the absence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. The particle creation rate is uniquely determined by the variation of gravitational and cosmological “constants”. We observe that the variable gravitational constant does not necessarily imply particle creation. In a generic situation, models can be interpolated between different phases of the universe. The dynamical behaviors of the solutions and kinematical parameters of the model are discussed in detail.