Satellite test for dragging of inertial frames

It is shown that it is possible by using the lack of synchronization of clocks by light signal synchronization in elliptical orbits to test for the dragging of inertial frames in Einstein's theory of general relativity. Possible experiments are discussed.     

Clock transport synchronization and the dragging of inertial frames for elliptical orbits

It is shown that is is possible to test for the dragging of inertial frames in Einstein's theory of general relativity by using the discrepancy between clocks synchronized by clock transport in elliptical orbits. Possible experiments are discussed.     

On the inertial mass concept in special and general relativity

Inertial mass in relativity theory is discussed from a conceptual view. It is shown that though relativistic dynamics implies a particular dependence of the momentum of a free particle on its velocityin special relativity, which diverges as v approaches c, the inertial mass itself of a moving body remains constant, from any frame of observation. However, extension to general relativity does conceptually introduce variability of the inertial mass of a body, through a necessarily generally covariant field theory of inertia, when the Mach principle is incorporated into the theory of general relativity, as a theory of matter.     

Electrodynamical origins of Einstein's theory of general relativity

The failure of the Newtonian theory of gravitation to satisfactorily account for the motion of Mercury's perihelion cannot be held to have justified the development of general relativity. This paper shows how the origins of general relativity were firmly embedded in contemporary attempts to introduce the new mechanics of special relativity into gravitational theory. These new theories of gravitation took as their basis the electrodynamical equations as formulated by Minkowski and attempted to represent the gravitational potential first by a vector and then by a scalar (in the four-dimensional sense). That Einstein chose the symmetric fundamental tensorg _ij as his gravitational potential is seen to have been both a natural and necessary development. With this viewpoint the full theory of general relativity can be seen to be remarkably similar to those theories of gravitation that preceded it. The paper also contains a previously unpublished letter written by Einstein to H. A. Lorentz.     

On the measurement of proper time in general relativity by means of atomic clocks

The quantity , which is called the proper time of a particle in the general theory of relativity, has the following meaning: it is the time measured by clocks moving with the particle. The question arises of how proper time is measured by real clocks. At present, atomic clocks are the most accurate, being stabilized by the frequency of intraatomic transitions. In the present paper, the stability of the reference frequency of such clocks is considered, i.e., the possible discrepancies between the proper time and the time measured by atomic clocks.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 99–102, January, 1981.     

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.     

On the use of clocks in satellites for the detection of gravitational radiation and oscillations of the sun

Summary It is shown that, by using the path dependence of synchronization of clocks in a gravitational field, it is in principle possible not merely to observe bursts of gravitational radiation but also oscillations of the Sun. Estimates are made of the effect of the solar oscillations on the clocks. It is also pointed out that, by making use of the binary pulsar and millisecond pulsars as clocks, it is possible to observe gravitational radiation without interference from the solar oscillation.

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Riassunto Si mostra che, usando la dipendenza del percorso di sincronizzazione degli orologi in un campo gravitazionale, è possibile, in linea di principio, osservare non soltanto impulsi di radiazione gravitazionale ma anche oscillazioni del Sole. Si fanno stime dell'effetto delle oscillazioni solari sugli orologi. Si sottolinea inoltre che facendo uso delle pulsar binarie e delle pulsar a millisecondi come orologi, è possibile osservare radiazioni gravitazionali senza interferenza da parte dell'oscillazione solare.

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Резюме Показывается, что использование зависимости синхрононизации часов от траектории в гравитационном поле, в принципе, позволяет не только наблюдать вспышки гравитационнного излучения, а также осцилляции Солнца. Оценивается влияние солнечных осцилляций на часы. Отмечаетсь, что использование бинарного пульсара и миллисекундных пульсаров в качестве часов, позволяет наблюдать гравитационное излучение вез интерференции от солнечных осцилляций.

     

On inertial frames in the theory of quantised fields

The physical significance of time symmetry and the difficulty of the definition of an inertia frame (reference frame) is considered for a quantum field of material points with special consideration of the electrodynamics of a superconducting body.     

On the two-body problem in general relativity

We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (∼1/c⁶ beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO and LISA type experiments.     

On general and restricted covariance in general relativity

We reconsider the principle of general covariance and give a rigorous formulation of a principle ofrestricted covariance. We give a number of examples of preferred coordinate systems, considered in the literature, and in each case demonstrate the applicability of the notion of restricted covariance proposed.     

On the symplectic structure of general relativity

The relation between the symplectic structures on the canonical and radiative phase spaces of general relativity is exhibited.Alfred P. Sloan Research Fellow. Supported in part by the NSF contract PHY80-08155 and by a grant from the Syracuse University Research and Equipment FundSupported in part by crédits ministériels, tranche spéciale     

On the vierbein formalism of general relativity

Both the Einstein–Hilbert action and the Einstein equations are discussed under the absolute vierbein formalism. Taking advantage of this form, we prove that the “kinetic energy” term, i.e., the quadratic term of time derivative term, in the Lagrangian of the Einstein–Hilbert action is non-positive definitive. And then, we present two groups of coordinate conditions that lead to positive definitive kinetic energy term in the Lagrangian, as well as the corresponding actions with positive definitive kinetic energy term, respectively. Based on the ADM decomposition, the Hamiltonian representation and canonical quantization of general relativity taking advantage of the actions with positive definitive kinetic energy term are discussed; especially, the Hamiltonian constraints with positive definitive kinetic energy term are given, respectively. Finally, we present a group of gauge conditions such that there is not any second time derivative term in the ten Einstein equations.     

On Birkhoff's theorem in general relativity

Two generalisations of Birkhoff's theorem are proved for the cases where the three-parameter group of motions acts on two-dimensional time-like and null orbits. A complete list of possible extensions of the three-parameter group to one of four parameters and of the resulting metrics is given.Turner and Newall Research Fellow.     

The use of algebraic computing in general relativity

In the past ten years various computer systems have been developed able to perform algebraic calculations. Unfortunately, the fact that there are ready to use, mostly easily attainable, computer languages and programs for manipulation of non-numerical algebraic data is often overlooked by potential users. Several investigations in general relativity have been performed using such systems in the past few years, and in many cases the calculations were of such a length that it would have been prohibitive to complete them without help from a computer. In the first part of the paper we discuss the type of calculations that can be performed by algebraic systems, and several of these relativistic calculations are very briefly reviewed by way of example. In the second and main part of the paper we present a comparative review of most of the leading algebraic systems. To make the comparison more concrete we have taken two calculations from relativity and programed them, as closely as possible, in the same way for all these systems. It is not necessary for a future user who wants to do the same kind of calculations for other metrics to learn the complete syntax of one of these languages. He can make a slight modification to one of our programs, which we are prepared to distribute.     

On the Newtonian limit of general relativity

We establish rigorous results about the Newtonian limit of general relativity by applying to it the theory of different time scales for non-linear partial differential equations as developed in [4, 1, 8]. Roughly speaking, we obtain a priori estimates for solutions to the Einstein's equations, an intermediate, but fundamental, step to show that given a Newtonian solution there exist continuous one-parameter families of solutions to the full Einstein's equations — the parameter being the inverse of the speed of light — which for a finite amount of time are close to the Newtonian solution. These one-parameter families are chosen via aninitialization procedure applied to the initial data for the general relativistic solutions. This procedure allows one to choose the initial data in such a way as to obtain a relativistic solution close to the Newtonian solution in any a priori given Sobolev norm. In some intuitive sense these relativistic solutions, by being close to the Newtonian one, have little extra radiation content (although, actually, this should be so only in the case of the characteristic initial data formulation along future directed light cones).Our results are local, in the sense that they do not include the treatment of asymptotic regions; global results are admittedly very important — in particular they would say how differentiable the solutions are with respect to the parameter — but their treatment would involve the handling of tools even more technical than the ones used here. On the other hand, this local theory is all that is needed for most problems of practical numerical computation.     

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.     

A plane symmetric solution of Einstein's field equations of general relativity containing zero-rest-mass scalar fields

An exact static solution of Einstein's field equations of general relativity in the presence of zero-rest-mass scalar fields has been obtained when both the metric tensor gijand the zero-rest-mass scalar field φexhibit plane symmetry in the sense of Taub [9]. Our solution generalizes the empty space-time solution with plane symmetry previously obtained by Taub to the situation when static zero-rest-mass scalar fields are present. The static plane symmetric solutoins of Einstein's field equations in the presence of massive scalar fields, and the difference between the massless and non-massless scalar fields are being investigated, and will be published separately later on. We also hope to discuss non-static plane symmetric solutions of Einstein's field equations in the presence of scalar fields in future.     

On the invariant mass conjecture in general relativity

An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, PolandSupported in part by the Polish Ministry of Science Research Project CPBP 01.2 and by the NSF Grant PHY8503072 to Yale University