Rigidly Rotating Dust in General Relativity

A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.     

On Average Properties of Inhomogeneous Fluids in General Relativity: Dust Cosmologies

For general relativistic spacetimes filled with irrotational dust a generalized form of Friedmann's equations for an effective expansion factor a _D of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the backreaction effect of inhomogeneities on the average expansion of the model. A universal relation between backreaction and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to a _D ^-2, the expansion law governing a generic domain can be found. However, as the general equations show, backreaction acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.     

Master Equation in the General Gauge: On the Problem of Infinite Reducibility

The master equation is quantized. This is an example of quantization of a gauge theory with nilpotent generators. No ghosts are needed for the generation of a gauge algebra. The point about nilpotent generators is that one can not write down a single functional integral for this theory. Instead, one has to write down a product of two coupled functional integrals and take a square root. In a special gauge where the gauge conditions are commuting, the functional integrals decouple and one recovers the known result.     

爱因斯坦场方程推导过程的逻辑梳理--纪念广义相对论发表100周年

爱因斯坦用了10年时间分5步从狭义相对论提升到广义相对论及引力场方程,本文对此过程进行了逻辑梳理并辅助解释推导过程。     

A Novel Dynamics Equation of Elastic Rotation Shaft Possessing Twin Side Based on the Theory of Relativity

A novel dynamics equation of elastic rotation shaft possessing twin side based on the theory of relativityis built in this paper. The equation is established in different coordinate systems, which can provide the foundationtheoretically and methods for the similarity engineering and the similarity calibration of instruments used for measuring,observing, and controlling.     

Derivation of Magnetized-Wire Metrics in 5-Dimensional General Relativity

An infinite class of magnetized line-source (wire) metrics are here derived within the 5D GR (Kaluza-Klein) formalism. These metrics are cylindrically-symmetric (thus representing line-sources), and off-diagonal (thereby representing magnetized wire sources). The off-diagonality of these metrics is significant as all prior cylindrically-symmetric 5D GR metrics have been diagonal. In Kaluza-Klein theory, the vector potentials of EM are incorporated into the extended off-diagonal components of the metric. Thus, examination of such off-diagonal line source (magnetized wire) metrics is a hitherto untapped potential for 5D GR investigation.     

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannot be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field,an equation of motion of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.     

An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity

No Heading In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear (in space). No inertial motion steps are considered. The rest clock is denoted as (1), the to and fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: (1) What is the effect of the finite force acting on (2) on the proper time interval ⁽²⁾ measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The special theory of relativity is used in order to describe the hyperbolic (in spacetime) motion of (2) in the frame I. (II) Is this effect an absolute one, i.e., does the accelerated observer A comoving with (2) obtain the same results as that obtained by the observer in I, both qualitatively and quantitatively, as it is expected? We use the general theory of relativity in order to answer this question. It turns out that _I = _A for both the clocks, ⁽²⁾ does depend on g = F/m, and = ⁽²⁾/⁽¹⁾ = (1 – ²atanhj)/ < 1. In it ; = V/c and V is the velocity acquired by (2) when the force is inverted.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

Development of the Evans Wave Equation in the Weak-Field Limit: The Electrogravitic Equation

The Evans wave equation [1-3] is developed in the weak-field limit to give the Poisson equation and an electrogravitic equation expressing the electric field strength E in terms of the acceleration g due to gravity and a fundamental scalar potential ⁽⁰⁾ with the units of volts (joules per coulomb). The electrogravitic equation shows that an electric field strength can be obtained from the acceleration due to gravity, which in general relativity is non-Euclidean spacetime. Therefore an electric field strength can be obtained, in theory, from scalar curvature R. This inference is supported by recent experimental data from the patented motionless electromagnetic generator [5].     

Plane Symmetric String Cosmological Model in Modified Theory of General Relativity

It is shown that homogeneous plane symmetric string cosmological model for Takabayasi string i.e. ρ=(1+ω)λ does not exist in Barber’s second self creation theory. Further it is found that the string cosmological model in this theory exist only when ω=0. Therefore model for ρ=λ (geometric string) is constructed. Some physical and geometrical properties of the model are discussed.     

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to study the classical motion of a mass point in gravitational gauge field.First,by using Mathematica,a spherical symmetric solution of the field equation of gravitational gauge field is obtained,which is just the traditional Schwarzschild solution.Combining the principle of gauge covariance and Newton's second law of motion,the equation of motion of a mass point in gravitational field is deduced.Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field,we can discuss classical tests of gauge theory of gravity,including the deflection of light by the sun,the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun.It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.     

Derivation of x 5-Dependent Charged Metrics in 5-Dimensional General Relativity

New classes of charged-source 5D GR (Kaluza-Klein) metrics are derived here. These metrics, unlike prior Kaluza-Klein metrics, are both off-diagonal (representing charged solutions), andx ⁵-dependent. The x ⁵-dependence, in particular, is important as modern 5D GR (Induced Matter) theory has abandoned the cylindrical restriction on the 5th dimension (requiring it be curled up very small), and, thus, allows the metric to have x ⁵-dependence. x ⁵-dependence, therefore, represents a hitherto untapped potential for 5D GR investigation.     

Nonperturbative Time-Independent Green Function of Matrix Schrödinger Equation. General Formalism and Quasiclassical Representation

A Green function of time-independent multichannel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multichannel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multichannel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multipotential system within quasiclassical approximation. The limits of strong and weak interchannel interactions are studied.Alexander I. Pegarkov:On leave from Physics Faculty     

Exact solutions to the time-dependent Lorentz gas Boltzmann Equation: The approach to hydrodynamics

New exact solutions to the time-dependent Lorentz gas Boltzmann equation are presented for two classes of nonequilibrium initial value problems: thedecay of localized disturbances and theresponse to applied electric fields. These exact results are used to gain some insight into the crossover of the nonequilibrium state from the early-timekinetic regime to the late-timehydrodynamic regime.     

Alternative Simulating Technique for Periodic Motion in the Presence of Multiplicative White Noise

An effective approach for simulating the periodic motion of an overdamped particle subjected to a multiplicative white-noise source is described. The accurate calculations for the velocity of the particle and its correlation function can be realized by introducing an inertial term. The results show that fluctuation around a time-averaged quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift. In particular, the present algorithm converges on the correct values of the calculated quantities, while the mass of the particle approaches to zero.     

From the Von-Neumann Equation to the Quantum Boltzmann Equation in a Deterministic Framework

In this paper, we investigate the rigorous convergence of the Density Matrix Equation (or Quantum Liouville Equation) towards the Quantum Boltzmann Equation (or Pauli Master Equation). We start from the Density Matrix Equation posed on a cubic box of size L with periodic boundary conditions, describing the quantum motion of a particle in the box subject to an external potential V. The physics motivates the introduction of a damping term acting on the off-diagonal part of the density matrix, with a characteristic damping time ^–1. Then, the convergence can be proved by letting successively L tend to infinity and to zero. The proof relies heavily on a lemma which allows to control some oscillatory integrals posed in large dimensional spaces. The present paper improves a previous announcement [CD].