Gravi-inertial reference frames in Schwarzschild and Kerr spaces

Gravi-inertial reference frames — the analogue of inertial frames in two-dimensional space — are constructed in Schwarzschild and Kerr spaces. With their help the energy, momentum, and angular momentum of these systems are determined. A form is found for writing Kerr's solution in Bondi-Sachs coordinates in the slow-rotation approximation. A new solution of Einstein's equations is found in this approximation which describes the gravitational field of a rotating and radiating source.     

Electrodynamic equations in noninertial reference frames

The formalism for analysis of exterior spatial differential forms developed by the present author is used to study the equations of electrodynamics in noninertial reference frames. General covariant differential and integral relationships which generalize the corresponding laws of classical three-dimensional electrodynamics in inertial reference frames are obtained.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 7, pp. 97–104, July, 1978.The author expresses his sincere gratitude to V. I. Rodichev for his constant interest in the study and valuable advice.     

Analytical mechanics in noninertial reference frames

The fundamental equations of the relativistic analytical mechanics of N gravitating bodies in noninertial reference frames are obtained with the application of the apparatus of three-dimensional tensor analysis.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–39, September, 1981.     

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois–Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: (a) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; (b) a polytropic distribution matched to a Schwarzschild exterior; (c) a Schwarzschild–Schwarzschild spacetime. The conservation of energy, the Newman–Penrose constant preservation and other expected features are observed.     

Tetrad formalism and reference frames in general relativity

This review is devoted to problems of defining the reference frames in the tetrad formalism of General Relativity. Tetrads are the expansion coefficients of components of an orthogonal basis over the differentials of a coordinate space. The Hamiltonian cosmological perturbation theory is presented in terms of these invariant differential forms. This theory does not contain the double counting of the spatial metric determinant in contrast to the conventional Lifshits-Bardeen perturbation theory. We explicitly write out the Lorentz transformations of the orthogonal-basis components from the cosmic microwave background (CMB) reference frame to the laboratory frame, moving with a constant velocity relative to the CMB frame. Possible observational consequences of the Hamiltonian cosmological perturbation theory are discussed, in particular, the quantum anomaly of geometric interval and the shift of the origin, as a source of the CMB anisotropy, in the course of the universe evolution.     

Inertial reference frames in Einstein's theory of gravitation

A physical definition of the inertial reference frame (IRF) is given, and the properties of solutions of the Einstein equation (with cosmological constant), which admit an IRF (IRF solutions) are investigated. Their Petrov type is uniquely determined by the viscous stress tensor. Only the typesI, D or 0 are possible. The unique vacuum IRF solution is the Minkowski space-time. The unique IRF solution belonging to a perfect fluid is the Einstein universe. is of special importance. For=0, the only physically admissible IRF solution is the Minkowski space-time. For0, only interior solutions with strong restrictions for density and pressure are possible.     

On dark energy and accelerated reference frames

The paper is devoted to an explanation of the accelerated rate of expansion of the Universe. Usually the acceleration of the Universe, which is described by FRW metric, is due to dark energy. It is shown that this effect may be considered as a manifestation of torsion tensor for a flat Universe in the realm of Teleparallel gravity. An observer with radial field velocity obey Hubble's Law. As a consequence it is established that this is radial acceleration in a flat Universe. In Eq. (35) the acceleration is written in terms of the deceleration parameter, the Hubble’s constant and the proper distance. This may be interpreted as an acceleration of the Universe.     

Causality, relativity and quantum correlation experiments with moving reference frames

Entanglement, one of the most important features of quantum mechanics, is at the core of the famous Einstein-Bohr philosophical debate [1] and is the principal resource for quantum information processing [2]. We report on new experimental investigations of the properties of entangled photon pairs with emphasis on the tension between quantum mechanics and relativity [3,4]. Entangled photons are sent via an optical fiber network to two villages near Geneva, separated by more than 10 km where they are analyzed by interferometers [5]. The photon pair source is set as precisely as possible in the center so that the two photons arrive at the detectors within a time interval of less than 5 ps (corresponding to a path length difference of less than 1 mm). This sets a lower bound on the ‘speed of quantum information’ to 10⁷ times the speed of light. Next, one detector is set in motion [6] so that both detectors, each in its own inertial reference frame, are first to do the measurement! The data always reproduces the quantum correlations.     

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically, we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy?Cmomentum tensor of the source is analyzed.     

Formalism of exterior forms and noninertial reference frames

A general covariant theory of exterior spatial forms is proposed and the fundamental differential operations are defined in a formalism whose basic object is the congruence of timelike curves specified in a space-time manifold.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–97, July, 1978.The author is sincerely grateful to Professor V. I. Rodichev for his constant interest in the work.     

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant Λ, and , by considering the case . This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case ) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors.     

Experimental verification of an Aharonov-Bohm effect in rotating reference frames

A thought experiment is reviewed which shows two things. First, in a region of a rotating frame that is not simply connected, the inertial forces can be canceled without completely canceling the inertial vector potential (whose curl determines the Coriolis force); second, the presence of this uncanceled potential can be detected in a quantum interference experiment. It is then argued that the thought experiment was realized in an earlier experiment involving a rotating superconductor, and that the experimental results confirm the theoretical prediction. In this way, the first experimental verification of a physical effect due to a nonelectromagnetic potential in a force-free region is established. An analogous experiment for the gravitational vector potential is also discussed. Finally, it is pointed out that the close connection between electromagnetic and inertial vector potentials provides an intuitive way to make predictions about rotating superconductors.     

Transformations between inertial and linearly accelerated frames of reference

Transformation equations between inertial and linearly accelerated frames of reference are derived and these transformation equations are shown to be compatible, where applicable, with those of special relativity. The physical nature of an accelerated frame of reference is unambiguously defined by means of an equation which relates the velocity of all points within the accelerated frame of reference to measurements made in an inertial frame of reference.     

不同参考系中多普勒效应公式的统一

由于所用参考系不同,因而各种文献给出了不同形式的多普勒效应表达式.本文通过洛伦兹变换,对不同参考系中多普勒效应公式给出了普遍推导,从而将它们统一起来.     

Lorentz invariance of gravitational Lagrangians in the space of reference frames

The recently proposed theories of gravitation in the space of reference framesS are based on a Lagrangian invariant with respect to the homogeneous Lorentz group. However, in theories of this kind, the Lorentz invariance is not a necessary consequence of some physical principles, as in the theories formulated in space-time, but rather a purely esthetic request. In the present paper, we give a systematic method for the construction of gravitational theories in the spaceS, without assuming a priori the Lorentz invariance of the Lagrangian. The Einstein-Cartan equations of gravitation are obtained requiring only that the Lagrangian is invariant under proper rotations and has particular transformation properties under space reflections and space-time dilatations     

Quantum-related reference frames and the local physical significance of potentials

In a sequel to our previous paper we discuss two thought experiments which show that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but, in singly connected portions of that region, also have a necessary local significance (via their quantum spread ΔA, which cannot be neglected). We then show, in continuation to the foregoing paper, how suchA arise “geometrically” as kinematic quantities associated with the transformation between “quantum-related” reference frames, e.g., when the relative frame velocities areq-numbers possessing a quantum spread.     

从4个参考系看弹射过程

从4个参考系分析了弹射过程.     

Noninvariant one-way speed of light and locally equivalent reference frames

We consider an isotropical inertial reference frame (“stationary”) and in it a uniformly rotating circular platform of radiusR. The velocity of light relative to the rim of the platform is calculated and found to have values necessarily different fromc. This remains the same ifR is increased but the peripheral velocity is kept constant. Since by so doing any small piece of the circumference can be considered better and better at rest in a (“moving”) inertial system, the velocity of light relative to this system can be deduced. Noninvariant values are obtained and shown to coincide with the predictions of our recently published “inertial transformations”.