Energy-momentum complex in Møller's tetrad theory of gravitation

Møller's tetrad theory of gravitation is examined with regard to the energymomentum complex. The energy-momentum complex as well as the superpotential associated with Møller's theory are derived. Møller's field equations are solved in the case of spherical symmetry. Twodifferent solutions, giving rise to thesame metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.     

On Møller's tetrad theory of gravitation. Gravitational radiation

In the background of Møller's theory, two energy-momentum complexest andP, are defined. From them, the losses of energy and angular momentum of a nongravitationally bound system due to the radiation of gravitational waves are evaluated. To solve the field equations some approximation procedures are used. The post-Newtonian limit is studied. When the modulus of the coupling constant of the theory is smaller than 10³ and some reasonable conditions are assumed, the results here obtained appear to be identical to those of general relativity. The work performed here would be basic when dealing with some important questions in generalizing Møller's theory.     

Møller's energy-momentum complex — Once again

The 35-year-old problem of Møller's energy-momentum four-vector when transformed by a global Lorentz transformation is discussed again. It is argued that Møller's result is adequate from the viewpoint of general relativity and hence does not defeat his energy-momentum complex.     

Spherically symmetric solutions in Møller's tetrad theory of gravitation

The general solution of Møller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.     

On Mø11er's tetrad theory of gravitation cosmology

We use a particular tetrad field to describe homogeneous isotropic cosmologies in the background of Møller's theory of gravitation. We prove that the universe can be closed or open for any possible value of the density of energy. The relation between the apparent magnitudem and the number of galaxies with a magnitude greater thanm is proved to be different from that of general relativity.     

A critical inquiry into the objection of Møller to his energy-momentum complex

In the year 1958 Møller derived an energy-momentum complex to attain the localizability of the energy in gravitational fields. However, three years later after extensive investigations he himself raised an objection to his expression showing that the corresponding energy-momentum vector of a closed physical system does not transform like a free 4-vector with respect to a Lorentz transformation. An inquiry into the objection of Møller is carried through at full length. Surprisingly it turns out that the equation on which he based his objection originates from a misinterpretation. Moreover, the argument given by him to explain the alleged failure of his expression proves to be incomplete. Complementing the argument, the objection of Møller is no longer tenable.     

Møller's tetrad theory of gravitation as a special case of Poincaré gauge theory—A coincidence?

Møller's tetrad theory of gravitation is included in Poincaié gauge theory for a special choice of parameters. In both theories the conservation theorems are derived from the field equations. They have the same form as in Einstein's theory. We compare the invariance properties of the field equations and discuss questions concerning the interpretation and measurability of the tetrad coefficients.     

Vacuum Non Singular Black Hole Solutions in Tetrad Theory of Gravitation

Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate and assuming a specific form of the vacuum stress-energy momentum tensor, a general solution of Møller's field equations in case of spherically symmetric nonsingular black holes is derived. The general solution is characterized by an arbitrary function and two constants of integration. The previously obtained solutions are verified as special cases of the general solution. The associated metric of the general solution gives no more than the spherically symmetric nonsingular black hole obtained before. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function, and is different from the standard one.     

On the scalar-tetradic theories of gravitation: Cosmology and gravitational radiation

The so-called scalar-tetradic theoriesA andB generalize Møller's theory of gravitation. In this work, some results previously obtained in Møller's theory are extended to the theoriesA andB. When the parametersW and ^*. of the theoryA are not too small (or large), the losses of energy and angular momentum of a nongravitationally bound system are proved to be the same as in general relativity. The basic equations of cosmology are derived and some topics are treated. In particular, any density of energy ₀ (10^–29 g cm^–3 ₀ 10^–31 g cm^–3) appears to be compatible with the observational values ofH ₀ (Hubble constant) andqo (deceleration parameter) in the theory A; thus, no intergalactic energy assumption is necessary.     

On the behavior of an oscillator clock near the singularity of a gravitational field

In 1975 Møller tried to show that the general relativistic concept of standard time or proper time would lose its physical meaning in the vicinity of singularities of a gravitational field [1]. His treatment of a classical harmonic oscillator clock falling into a singularity is checked in the present paper and is found to be insufficient to prove the above statement. A relativistic clock model is given to ensure the reasonable physical meaning of proper time.     

Møller was right

Direct calculation proves that the total energy-momentum vector derived from the Møller energy-momentum complex from 1958 does not transform like a free 4-vector with respect to the Lorentz transformation. This conforms with the conclusion formulated by Møller himself, but it contradicts the result of the critical analysis of Kovacs. Defects in Kovacs argumentation are found.     

Møller operators for scattering on singular potentials

The existence of Møller operators is proved for singular potentials which decrease more rapidly at infinity than the Coulomb potential. The question of their uniqueness is discussed.     

Rotating frames in special relativity analyzed in light of a recent article by M. Strauss

The argument of Einstein for non-Euclidity on a rotating disk is analyzed and found valid. The kinematic reason for the non-Euclidean geometry is stated explicitly and provides a kinematic resolution of Ehrenfest's paradox. The transformation from an inertial frameK to a rotating frame, the axis of which is at rest inK, is discussed. It is concluded in favor of the Galilean-like transformation employed by Møller. The method used by Møller in obtaining the intrinsic spatial geometry in any frame is examined. It is found to be adequate, provided that only coordinates with a proper metrical significance are used. In this connection the distinction between global and local geometry is found to be essential.     

Asymptotic triviality of the Møller operators in Galilei invariant quantum field theories

Asymptotic triviality of the Møller operators is shown for fermions interacting via nonlocal pair-potentials with a momentum cut-off. Such systems have stable Hamiltonians, defining the time evolution in the Heisenberg representation, and strong mixing properties.     

The equivalence of the Tolman and the Møller mass-energy formulae in general relativity

It is shown that, for time independent fields, the two seemingly different and unrelated Tolman and Møller mass-energy formulae in general relativity are, in fact, completely equivalent.This paper is humbly dedicated to the late Mr. S.P. Christodoulides, my mathematics teacher of long ago.     

Dual observers in operational relativity

We give a tensor formulation of synchronization transformations within special relativity in order to bridge the gap between some philosophical discussions (e.g., by Grünbaum and Winnie) and the analyses given by physicists (e.g., Møller). As an application, we discuss a physical interpretation of the duality between covariant and contravariant indices in the tensor formulation.     

(CuIn)_n(n=1,2)小团簇的结构与稳定性的从头算理论研究

本文采用从头算理论MP2方法研究了合金团簇(Cu In)n(n=1,2)的结构和稳定性.计算得到的双原子分子Cu In几何参数、频率和解离能跟实验数据十分吻合.(Cu In)2团簇有五个稳定结构,基态结构是具有1A1/C2v对称性的蝴蝶结构,结合能为6.57 e V.将计算结果与同族元素体系(Cu Al)2和(Cu Tl)2对比,无论是在构型上,还是在电子特性上都有相似性.文中给出了(Cu In)2稳定构型的电子结合能能谱,希望在实验上得以验证.     

A cluster study of aluminum adsorption on Ga-rich GaAs(100)(2 × 1) and β (4 × 2) surfaces

Ab initio self-consistent total energy calculations using second order Møller-Plesset perturbation theory and Hay-Wadt effective core potentials with associated basis sets (HWECP’s) for gallium and arsenic have been used to investigate the chemisorption properties of atomic aluminum on the Ga-rich GaAs(100)-(2 × 1) and β(4 × 2) surfaces. Finite sized hydrogen saturated clusters with the experimental zinc-blende lattice constant of 5.654 Å and the energy optimized Ga dimer bond length of 2.758 Å have been used to model the semiconductor surface. To investigate the effects of the core electrons of aluminum in the adsorption process, we have represented the Al adatom with both HWECP’s and an all electron 6-311++G** basis set. Detailed energetics of chemisorption on the (100) surface, including chemisorption energies, nearest surface neighbor bond lengths, and Mulliken population analysis, have been reported for all considered sites of chemisorption.     

Tomographic approach to the violation of Bell's inequalities for quantum states of two qutrits

The tomographic method is employed to investigate the presence of quantum correlations in two classes of parameter-dependent states of two qutrits. The violation of some Bell's inequalities in a wide domain of the parameter space is shown. A comparison between the tomographic approach and a recent method elaborated by Wu, Poulsen, and Mølmer shows the better adequacy of the former method with respect to the latter one.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.