Field Equations Of Relativity Research Articles

Nonlinear dynamics in the relativistic field equation

Abstract We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation ( h = G ˙ / G > 0 ) and open ( ζ = −1) universe. In other cases ( h ≦ 0, ζ = 0 and ζ = +1), there occurs non-chaotic behaviors. We have shown the following properties of the Friedmann chaos: (1) the sensitive dependence of solutions on the initial values ( x 0 and x ˙ 0 ) and the parameters ( a , b , c and d ); (2) the self-similarity of solutions in the x – x ˙ plane and the x – ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E -infinity theory.

The distribution and origination of electric field and charge in interface layer of superconductor

Based on relativistic field equations of superconducting state, the structure and forming mechanism of interface layer of superconductor are studied for the condition of weak magnetic field. It is shown that electric field, potential difference, Hall effect and sandwich of charge density exist in this layer,which originate from the measurable effect of potential field limited by relativistic covariance. In order to verify the result of this paper, a design of experiment is given.

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

RELATIVISTIC SUPERDENSE STAR MODELS OF PSEUDO SPHEROIDAL SPACE–TIME

The physically viable models of compact stars like SAX (J1808.4-3658) can be obtained using Vaidya–Tikekar ansatz prescribing spheroidal geometry for their interior space–time. We discuss here the suitability of an alternative ansatz in this context. The models of superdense star are proposed using a general three parameter family of solutions of relativistic field equations obtained adopting the alternative ansatz. The setup is shown to admit physically viable models of superdense stars and strange matter stars such as Her. X-1.

Relativistic solitons and superluminal signals

Envelope solitons in the weakly nonlinear Klein–Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.

Relativistic solitons and superluminal signals

Abstract Envelope solitons in the weakly nonlinear Klein–Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.

Klein Paradox in Spatial and Temporal Resolution

Based on spatially and temporally resolved numerical solutions to the relativistic quantum field equations, we provide a resolution to the controversial issue of how an incoming electron scatters off a supercritical potential step and how the electron-positron pair production is affected by this collision. The treatment of the problem as a correlated three-particle problem suggests revealing insight into the process.

Pairing correlations and resonant states in the relativistic mean field theory

We present a simple scheme for taking into account the resonant continuum coupling in the relativistic mean field-BCS calculations. In this scheme, applied before in nonrelativistic calculations, the effect of the resonant continuum on pairing correlations is introduced through the scattering wave functions located in the region of the resonant states. These states are found by solving the relativistic mean field equations with scattering-type boundary conditions for the continuum spectrum. The calculations are done for the neutron-rich Zr isotopes. It is shown that the sudden increase of the neutron radii close to the neutron drip line, the so-called giant halo, is determined by a few resonant states close to the continuum threshold.

ISOSPIN DEPENDENCE OF GROUND STATE PROPERTIES OF A=20 ISOBARS

The ground state nucleon (neutron and proton) distributions for A=20 isobars (Z=6–12) are investigated. For this purpose, the relativistic mean field equations are solved in the coordinate space and also by using the conventional basis expansion method. The pairing is treated in the simple constant gap approximation and also self consistently through the Bogoliubov transformation employing the realistic Gogny D1S interaction as well as the zero range density dependent effective interaction. The comparative study of the results thus obtained indicates the level and the extent of differences in the physical observables like binding energies, sizes, densities, etc. of these nuclei, arising due to the use of these different variants of solving the RMF/RHB equations. Though the results are qualitatively similar, the deviations do appear at a finer level, especially for large Tz (20 O and 20 N ). The calculations also reveal mirror symmetry about Tz=0 for all physical observables, which is in accordance with the experiment. The calculated nucleon densities are compared with those obtained by using a semi-phenomenological model that incorporates correctly the asymptotic behavior. The reaction cross-sections with these A=20 isobars as projectiles incident on a 12 C target at 950 A MeV incident energy, calculated within the Glauber model using the RMF/RHB and model densities agree well with the experiment.

Realistic neutrino opacities for supernova simulations with correlations and weak magnetism

Advances in neutrino transport allow realistic neutrino interactions to be incorporated into supernova simulations. We add tensor couplings to relativistic random phase approximation calculations of neutrino opacities. Our results reproduce free-space neutrino-nucleon cross sections at low density, including weak magnetism and recoil corrections. In addition, our opacities are thermodynamically consistent with relativistic mean field equations of state. We find antineutrino mean free paths that are considerably larger then those for neutrinos. This difference depends little on density. In a supernova, this difference could lead to an average energy of ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ that is larger than that for ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ by an amount that is comparable to the energy difference between ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\overline{\ensuremath{\nu}}}_{e}.$

Bianchi type I string cosmologies

By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present some classes of solutions of general relativistic field equations which describe cosmological string-dust models in Bianchi type I space-time. Some of the classes of models obey Takabayashi’s equation of state whereas a class of models exhibits inflation in the initial stage. Two of the classes presented here have Kasner’s space-time as past asymptote

Surface structure of strange superheavy nuclei

Bound, strange, neutral superheavy nuclei, stable against strong decay, may exist. A model effective field theory calculation of the surface energy and density of such systems is carried out assuming vector meson couplings to conserved currents and scalar couplings fit to data where it exists. The nonlinear relativistic mean field equations are solved assuming local density baryon sources. The approach is calibrated through a successful calculation of the known nuclear surface tension.

Some stochastic aspects of quantization

From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic field equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrodinger equation.

Apparent superluminal behavior in wave propagation

The apparent superluminal propagation of electromagnetic signals seen in recent experiments is shown to be the result of simple and robust properties of relativistic field equations. Although the wave front of a signal passing through a classically forbidden region can never move faster than light, an attenuated replica of the signal is reproduced ``instantaneously'' on the other side of the barrier. The reconstructed signal, causally connected to the forerunner rather than the bulk of the input signal, appears to move through the barrier faster than light.

Hydrodynamic approach to the interaction of a relativistic ultrashort laser pulse with an underdense plasma.

The interaction of an ultrashort, high peak power laser pulse with an underdense plasma is investigated within a physical model based on the three-dimensional cold hydrodynamic approach, which allows one to study the dynamics of the laser pulse and of the generated wakefields self-consistently, in the fully relativistic, strongly nonlinear regime. Our model is developed with the aim of describing very short laser pulses (with l(0)<lambdap and l(0)<<l perpendicular, where l(0),l perpendicular, lambdap are the pulse length, its transverse scale, and the plasma wavelength, respectively) down to single cycle radiation wave packets, which have become available with the recent progress in laser technology. The space-time structure and the evolution of large quasistatic electric and magnetic fields are studied, together with the pulse dynamics, by the direct numerical integration of the relativistic fluid and field equations, within the extended paraxial approximation.

A Computer Aided Study of Resonant Cap Impatt Amplifiers using Radial Line Approach

A computer aided numerical iteration technique is presented which would be suitable for optimum design and realisation of Impatt amplifiers with circular resonant cap cavities. The dependence of the centre frequency of the amplifier on the device and circuit impedance with the device placed at the centre of the circular resonant cap cavity has been studied. The real part of the impedance seen at the cap edge by an incoming signal has been studied along with the geometrical parameters of the cavity using a numerical iteration process through solution of related electromagnetic field equations. The dependence of the centre frequency on the cap radius, cap height, post radius and the cap thickness has also been studied.

B-spline finite elements and their efficiency in solving relativistic mean field equations

A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled nonlinear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.

Relativistic field equations from higher-order polarizations of the poincaré group

The theory of free relativistic fields is shown to arise in a unified manner from higher-order, configuration-space, irreducible representations of the Poincaré group. A de Sitter subalgebra, in the massive case, and a Poincaré subalgebra, in the massless case, of the enveloping algebra of the Poincaré group are the suitable higher-order polarizations. In particular, a simple group-theoretic derivation of the Dirac equation is given.

COSMOLOGICAL MASSIVE SCALAR FIELD INTERACTING WITH VISCOUS FLUID

Relativistic cosmological field equations are obtained for a Robertson-Walker space time interacting with viscous fluid and massive scalar field. The cosmological solutions to the field equations are obtained and the nature of the scalar field as well as the viscous fluid are studied. It is found that the solutions obtained are realistic only for a closed Universe.

Yang-Mills inspired solutions for general relativity

Several exact, stationary axisymmetric solutions to Einstein's vacuum equations are given. These solutions were found using the connection between Yang-Mills theory and general relativity. Taking known solutions of the Yang-Mills equations (e.g. the topological BPS monopole solutions) it is possible to construct exact solutions to the general relativistic field equations. Although the general relativistic solutions were found starting from known solutions of Yang-Mills theory they have different physical characteristics.