Showing papers on "Four-force published in 1966"
TL;DR: In this article, an approach to study the dynamics of thin shells of dust in general relativity is presented. But no mention of admissible or even any space-time co-ordinates is needed.
Abstract: An approach to shock waves, boundary surfaces and thin shells in general relativity is developed in which their histories are characterized in a purely geometrical way by the extrinsic curvatures of their imbeddings in space-time. There is some gain in simplicity and ease of application over previous treatments in that no mention of « admissible » or, indeed, any space-time co-ordinates is needed. The formalism is applied to a study of the dynamics of thin shells of dust.
2,347 citations
TL;DR: In this article, the similarities between the diagram of Kruskal space in general relativity and that of the uniformly accelerated rigid rod in special relativity are shown to be the result of certain physical similarities.
Abstract: The striking formal similarities between the diagram of Kruskal space in general relativity and that of the uniformly accelerated rigid rod in special relativity are shown to be the result of certain physical similarities.
319 citations
TL;DR: Theories of gravitation similar to General Relativity but with an additional R2 term in the Lagrangian are explored in this article. But the experimental consequences of R2 terms are investigated.
Abstract: Theories of gravitation similar to General Relativity but with an additionalR2 term in the Lagrangian are explored. The Schwarzschild metric is not the exterior solution that can be continued to the interior of the body to give a positive definite mass distribution. The experimental consequences ofR2 terms are investigated. Furthermore, it is shown that a theory with anR2 term only possesses an interesting singular dependence on the coupling constant.
102 citations
01 Jan 1966
61 citations
01 Jan 1966
39 citations
30 citations
23 citations
18 citations
TL;DR: In this paper, the authors showed that the first-order formula for travel time in the circular-orbit model is strictly independent of the nonlinear term in the theory of general relativity.
Abstract: Using a model of circular coplanar orbits and an analysis accurate to first order in the sun's gravitational radius, Ross and Schiff discussed the recent proposal to test general relativity by measuring round-trip travel times of radar pulses transmitted from the earth towards an inner planet. Their main conclusion, that such measurements would be sensitive to a nonlinear term in Einstein's theory, we find to be invalid. Since first-order differences between Newtonian and Einsteinian orbits are well known to depend on a nonlinear term in the metric, one might expect the round-trip travel times also to depend in first order on such a term. Curiously, this expectation is not realized for circular orbits. When expressed as a function solely of clock readings, the first-order formula for travel time in the circular-orbit model is strictly independent of the nonlinear term. Even were the combined use of radar-pulse travel times and the results of "exact" optical measurements envisioned, their sensitivity to this nonlinear term would be masked almost completely by unavoidable uncertainties in the estimates of other unknown parameters such as the mass of the sun. For noncircular orbits, however, the travel-time measurements will be noticeably sensitive to this nonlinear term through its effect on the advance of the perihelion. In addition to re-examining the circular-orbit model, we describe the operational procedures that we have developed for testing general relativity with data obtained from actual planetary observations. These data cannot be expected in the near future to provide a significant test of more than the first-order influence of solar gravity on radar-pulse travel times and the non-Newtonian advance of Mercury's perihelion, as we previously pointed out.
01 Aug 1966
TL;DR: The lectures were given to graduate and undergraduate engineering and science students during the spring semester of 1966 as discussed by the authors. The lectures cover both the special and general theories, and the coverage of the special theory is fairly complete while that of the general theory is somewhat abbreviated due to lack of time.
Abstract: : The lectures were given to graduate and undergraduateengineering and science students during the spring semester, 1966. The lectures cover both the special and general theories. The coverage of the special theory is fairly complete while that of the general theory is somewhat abbreviated due to lack of time. The lectures on the general theory stopped with the derivation of the Schwartzschild solution and a discussion of the linear theory. (Author)
TL;DR: In this article, the formulation of the general theory of relativity in terms of the Lorentz principle is attempted and it is shown that the principle in its ordinary form remains valid for such regions.
Abstract: This paper is the first of a series in which the formulation of the general theory of relativity in terms of the Lorentz principle is attempted. In this first part the Lorentz transformation is generalized so as to be applicable to parts of space where light is propagated homogeneously but possibly unisotropically. It is shown that the Lorentz principle in its ordinary form remains valid for such regions.
TL;DR: The principle of relativity applied to purely length-time considerations is shown to lead rigorously to either the Lorentz or the Galilean transformations, but to no other.
Abstract: The principle of relativity applied to purely length-time considerations is shown to lead rigorously to either the Lorentz or the Galilean transformations, but to no other. No reference is made to properties of light or of mass. The derivation itself leads to the appearance of an invariant and ultimate speed k as a constant of integration.
TL;DR: In this paper, the relation between Hamiltonian dynamics and the representation of relativitic invariance groups is explored, in particular the preservation of canonical Poisson bracket relations (the analog to canonical commutation relations) is a strong additional requirement on some types of relativity transformations (like the Lorentz rotation).
TL;DR: In this article, a method of obtaining Komar's covariant formulation of the conservation laws of general relativity directly from the variation of the scalar curvature density is presented, free of the addition of arbitrary elements and only tensorial terms and operations are employed in the development.
Abstract: A method of obtaining Komar's covariant formulation of the conservation laws of general relativity directly from the variation of the scalar curvature density is presented. The procedure of obtaining this expression is free of the addition of arbitrary elements and only tensorial terms and operations are employed in the development.
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TL;DR: Spinors have in recent years become an important mathematical tool in special and general relativity as discussed by the authors, and it is shown why spinors are the basic building bricks of any Lorentz invariant law.
Abstract: Spinors have in recent years become an important mathematical tool in special and general relativity. After a general review of the status of physical laws, it is shown why spinors are the “basic building bricks” of any Lorentz invariant law. The properties of spinors are briefly discussed and it is shown why it sometimes pays to translate a tensor problem into spinor language, solve it therein, and finally translate back.
TL;DR: The Rayski method was used to calculate the energy of a static and spherically symmetric gravitational system as mentioned in this paper, which was used for the first time in the 1990s.
Abstract: The Rayski method is used to calculate the energy of a static and spherically symmetrical gravitational system.
TL;DR: In this article, the relationships between Witten and Penrose and Bergmann's spinor approach to the theory of general relativity were analyzed. But the relationships were not discussed in detail.