Field Equations Of Relativity Research Articles

Relativistic numerical model for close neutron-star binaries.

We describe a numerical method for calculating the (3+1)-dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial three-metric chosen to be conformally flat. Against this solution to the general relativistic field equations, the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole ($l=4$) order including both mass and current moments and a correction for the slow-motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution. In the present work we illustrate the method by applying this model to evaluate various orbits of two neutron stars with a gravitational mass of $1.45{M}_{\ensuremath{\bigodot}}$ near the time of the final merger. We discuss the evidence that, for a realistic neutron-star equation of state, general relativistic effects may cause the stars to individually collapse into black holes prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated.

CANONICAL QUANTIZATION OF NONLOCAL FIELD EQUATIONS

We consistently quantize a class of relativistic nonlocal field equations characterized by a nonlocal kinetic term in the Lagrangian. We solve the classical nonlocal equations of motion for a scalar field and evaluate the on-shell Hamiltonian. The quantization is realized by imposing Heisenberg’s equation, which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincaré group. We also consider the Gupta-Bleuler quantization of a nonlocal gauge theory and analyze the propagators and the physical modes of the gauge field.

Modeling lossy anisotropic dielectric waveguides with the method of lines

This paper presents a new formulation useful for modeling waveguides constructed from lossy inhomogeneous anisotropic media. Our approach is based on a pair of Sturm-Liouville type wave equations that have been derived to handle inhomogeneous, diagonalized complex permittivity and permeability tensors. The method of lines is then applied to these wave equations, and related field equations, creating an indirect eigenvalue problem that correctly models this class of structure. Some refinements to the method of lines are also proposed, particularly, regarding the construction of the modal matrices found in the eigenvalue problem. Using our approach, modal dispersion curves have been computed for millimeter-wave and optical structures. Comparisons made with results available from the literature validate our approach.

Uniform radial motion of sound in a relativistic fluid ball

We present a new class of spherically symmetric exact solutions of the general relativistic field equations. These solutions describe perfect fluid balls with infinite central pressure and central density though their ratio is finite. A member of the class has been studied in detail from which we have constructed a model of causal fluid ball with constant sound speed.

ON THE FORM OF LOCAL CONSERVATION LAWS FOR SOME RELATIVISTIC FIELD THEORIES IN 1 + 1 DIMENSIONS

We investigate the possible form of local translation-invariant conservation laws associated with the relativistic field equations [Formula: see text] for a multicomponent field ϕ. Under the assumptions that (i) the vi' s can be expressed as linear combinations of partial derivatives ∂wj / ∂ϕk of a set of functions wj (ϕ), (ii) the space of functions spanned by the wj' s is closed under partial derivations, and (iii) the fields ϕ take values in a simply connected space, the local conservation laws can be transformed either to the form [Formula: see text] (where [Formula: see text] and [Formula: see text] are homogeneous polynomials in the variables [Formula: see text]), or to the parity-transformed version of this expression, [Formula: see text].

PARAMETRIC SPINOR APPROACH TO GRAVITY

It is shown that the gravitational field in general relativity has the properties of a parametric manifold, a mathematical structure generalizing the concept of gauge fields. A theory of parametric spinors is developed which contains, as a limiting case, spinor fields of unitary groups in Riemannian manifolds. Transition from the familiar [Formula: see text] spinor formalism to the parametric picture makes it possible to obtain a reparametrization-invariant decomposition of the gravitational equations with respect to a non-null congruence. This new formulation of the relativistic field equations appears to be amenable to canonical quantization, and provides more versatility in the treatment of phase-space variables.

Shear-free spherically symmetric perfect fluid solutions with conformal symmetry

In 1987, Dyer, McVittie and Oattes determined the general relativistic field equations for a shear-free perfect fluid with spherical symmetry and a conformal Killing vector in thet-r plane, which depend on an arbitrary constantm. Two particular solutions of these equations were given recently by Maharaj, Leach and Maartens, as well as a partial solution thought to be valid for almost allm. In this paper, this solution is completed for four values ofm, and it is shown that it cannot be completed for any others by currently available techniques; however, a new solution of a different form, but also depending on a Weierstrass elliptic function, is found for a further value ofm. None of these metrics are conformally flat; one of them has a constant expansion rate.

Novel quantization phenomenon for relativistic wave equations.

An unexpected phenomenon is shown to arise in the theory of relativistic wave equations. We study the canonical quantization of the Oppenheimer equations with standard creation and annihilation operators. The quantized fields satisfy the original relativistic field equations. Surprisingly, however, in the quantized theory relativistic invariance breaks down completely. Indeed, the two-point function is not relativistically invariant and there is no unitary representation of the Lorentz group.

Wave Function Collapse as a Real Physical Phenomenon Caused by Vacuum Fluctuations Near the Planck Scale

Abstract It is hypothesized that the collapse of the wave function is a real physical phenomenon caused by vacuum fluctuations near the Planck scale. The hypothesis is suggested by a recently proposed model (Planck aether model) according to which the fundamental kinematic symmetry is the Galilei-group with the Lorentz invariance as a derived dynamic symmetry. The proposed model has the goal to derive all fields and their interactions from an exactly nonrelativistic operator field equation, resembling Heisenberg's relativistic spinor field equation. In this model the groundstate of the vacuum is a superfluid consisting of an equal number of positive and negative Planck masses interacting via delta function potentials and making the cosmological constant equal to zero. Gauge bosons come from transverse waves propagating in a lattice of quantized vortices, and spinors are explained in this model as exciton-like quasiparticles held together by gauge bosons. Because vector gauge bosons move in the model with the velocity of light, objects held together by the forcc fields of these bosons obey Lorentz invariance as a dynamic symmetry. With the longitudinal wave modes moving with a superluminal phase velocity at energies near the Planck scale, it is conjectured that the quantum mechanical wave function is real and that its collapse results from the entrapment of the wave function by these longitudinal superluminal wave modes. Because these modes occur near the Planck scale their very large zero point fluctuations might therefore trigger the collapse even through dense matter. But because the fluctuations are finite, and because the wave modes have a finite albeit very large phase velocity, the quantum mechanical correlations would be broken above a ccrtain finite length. In the limit of a vanishing Planck length, and hence vanishing gravitational constant G, the phase velocity would become infinite, and the same would be true for the length above which the correlations are broken. One therefore may say that in the limit G = 0 the collapse is infinitely fast and that in this limit the correlations are not broken even over arbitrarily large distances

Cosmological mass model in general relativity

Relativistic cosmological field equations are obtained for a non-static stationary Bertotti-Robinson-type space-time for interacting perfect fluid and electromagnetic field. The cosmological solution to the field equations are obtained and the nature of the electromagnetic field as well the perfect fluid are studied. The electromagnetic field generated here corresponds to a special generic case and the perfect fluid distribution degenerates into a barotropic perfect fluid with equation of statep+ρ=0, ρ>0. It is shown here that the interacting barotropic fluid can generate gravitation only when the cosmological constant λ being a function ofx in a dynamic field.

Minimally relativistic Newtonian gravity

Special relativity is introduced into the theory of Newtonian gravity in a systematic manner. The modifications of Newtonian gravity that are made can be seen to be minimal for special relativistic covariance. Space is assumed to be flat. Particle trajectories are determined from a Hamiltonian formulation with a tensor potential hμν. The tensor nature of the potential is justified by requiring Lorentz covariance alone. Nongeneral relativistic field equations for the hμν are obtained. The static, spherically symmetric solutions of these equations are shown to produce the correct values for the precession of the orbit of Mercury and the bending of light near the Sun.

New approaches to the axisymmetric vacuum

The relativistic field equations of the axistationary vacuum are derived in Ernst coordinates in full detail. The derivation of the Kerr metric is given from the field equations.

Derivation of the formalism for neutrino matter oscillations from the neutrino relativistic field equations.

We derive the standard formalism of Mikheyev, Smirnov, and Wolfenstein for the oscillation of neutrinos in matter taking into account the Lorentz and second-quantized structure of the neutrino fields. We consider neutrinos with Dirac or Majorana masses.

Consistency of field equations in ?Self-Creation? cosmologies

It is pointed out that the field equations in one of Barber's two “self-creation” cosmologies are not only in disagreement with experiment, but are actually inconsistent, in general. The construction of consistent general relativistic field equations involving field variables, such asϕ, without invoking Lagrangian techniques, requires careful checking that sufficient functional freedom has been provided so as to produce a consistent set of equations.

String generated by massless fields

It is shown that relativistic field equations for massless particles of spin j = 1 2 , 1 and 2 possess a class of solutions which generate in a natural manner the string's coordinates X μ ( τ, σ), which satisfy the string field equation and the string constraint equations.

Relativistic field equations and the Painlevé test

The Painleve test for classes of relativistic field equations is performed. The connection with the complete integrability is discussed.

SOUND-LIKE COLLECTIVE MODE EXCITATION WITH PION ABSORPTION IN NUCLEAR MATTER

The relativistic mean field theory consistent with bulk properties of nuclear matter is extended to study the excitations of the sound-like collective modes in nuclear matter. Corresponding relativistic mean field equations are solved numerically and self-consis-tently. The effective mass of nucleon the speed of the sound and the amplitude of the sound-like solution are calculated. When the nuclear density is near or greater than the saturation density, the sound-like non-trivial solution could be found.

Casimir effect and gravitational collapse

The gravitational collapse of a singular spherically symmetric shell is studied when the shell, in addition to gravitational forces, is acted upon by repulsive surface forces of the type encountered in the theory of the Casimir effect (vacuum fluctuations). The analysis is based upon the following assumptions: 1) The local Casimir energy density does not gravitate,i.e. does not contribute to the total energy-momentum tensor in Einstein’s equations. 2) The influence from the Casimir force is taken into account by adding an extra term «by hand» in the radial equation of motion. Our treatment is accordingly not fully relativistic. The new equation of motion predicts that the shell is unable to collapse beyond a specific minimum radiusR min, under ordinary circumstances being of the same order of magnitude as the Compton wavelength of the shell. As the present theory is not based upon the relativistic field equations, there is no conflict with the gravitational singularity theorems.

Gödel‐type universe with a perfect fluid and a scalar field

The paper contains, along with a brief review of solutions of general relativistic field equations when the metric is of a particular cylindrically symmetric stationary form, a new solution of the same general category when the energy‐momentum tensor is due to a perfect fluid plus a scalar field. It turns out that under these constraints, the space‐time is completely homogeneous and contains closed timelike lines. There is, however, a nonuniqueness in the interpretation as one can introduce a Maxwellian electromagnetic field of arbitrary strength along with the perfect fluid and the scalar field.

Spinning fluids in general relativity

General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.