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1.
The physical foundations of the nonholonomic formulation of general relativity are determined, and the role of the Fock-Ivanenko coefficients in setting up and developing the tetrad formalism in general relativity is discussed. The physical and geometrical meaning of the nonholonomic transformations used in general relativity is determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 55–60, December, 1974. 相似文献
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S. Brian Edgar 《General Relativity and Gravitation》1980,12(5):347-362
The sets of equations that form the basis for the tetrad formalism approach in general relativity contain considerable redundancy. Papapetrou has determined this redundancy explicitly in the form of three sets of identities and employed these in investigations of the Newman-Penrose tetrad formalism. In this paper Papapetrou's work is reviewed and some of his results that do not seem to be well known are emphasized, along with some general implications. The main new result that is established concerns the Geroch-Held-Penrose formulation of the tetrad formalism. When the sets of equations that are usually used in this formulation are considered in the light of Papapetrou's identities, it is found that certain formal simplifications can be made and that the Geroch-Held-Penrose formulation can be presented more concisely. It is emphasized that the results in this paper apply in the most general case only. Any special cases (e.g., simplified tetrad and/or Riemann tensor) need to be considered separately. 相似文献
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I. M. Dozmorov 《Russian Physics Journal》1972,15(9):1246-1251
A generalization of the invariant criterion for pure gravitational radiation which was presented earlier is carried out in the tetrad formalism of the general theory of relativity. Its connection with the Petrov algebraic classification and other criteria based on it is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 15–20, September, 1972.In conclusion the author would like to thank Rodichev and Ivanenko for their constant interest in his work, and also the members of the gravitational seminars directed by Ivanenko, Levashev, and Sokolik for valuable critical observations on the questions here discussed. 相似文献
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Horst-Heino von Borzeszowski Hans-Jürgen Treder 《General Relativity and Gravitation》1993,25(3):291-306
The canonical approach to general relativity in terms of reference systems is discussed to show that Einstein's principles of equivalence and general relativity imply the physical insignificance of quantized general relativity. In particular it is demonstrated that even the (anholonomic) flat-space canonical formalism leads to physically uninterpretable results. This lack of quantum content of general relativity is reflected by Rosenfeld's uncertainty relations and can especially be removed by modifying general relativity in the spirit of classical Einstein-Cartan theory with teleparallelism. 相似文献
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Myron W. Evans 《Foundations of Physics Letters》2004,17(1):25-47
The first and second Maurer-Cartan structure relations are combined with the Evans field equation [1] for differential forms to build a grand unified field theory based on differential geometry. The tetrad or vielbein plays a central role in this theory, and all four fields currently thought to exist in nature can be described by the same equations, the tangent space index of the tetrad in general relativity being identified with the tetrad's internal (gauge group) index guage theory. 相似文献
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V. N. Tunyak 《Russian Physics Journal》1976,19(5):599-602
A general definition of the spin moment is presented in the tetrad formulation of the relativistic theory of gravitation; it is based on the conditions for the invariance of the corresponding action integral relative to infinitesimal tetrad transformations (the so-called tetrad spin moment) and infinitesimal coordinate transformations (the so-called coordinate spin moment). It is shown that the tetrad formulation of the general theory of relativity (TFGTR) and the tetrad theory of gravitation (TTG) in a space of absolute parallelism lead to fundamentally different definitions of spin, since in the Riemannian geometry of the TFGTR only the coordinate spin moment is physically meaningful, whereas in the space of absolute parallelism of the TTG only the tetrad spin moment has essential significance. It is also indicated that the Pellegrini-Plebanski theory (PPT) leads to an unsatisfactory hybrid definition of spin in the form of the coordinate spin moment of the gravitational and boson fields and the tetrad spin moment of the gravitational and fermion fields, the gravitational field entering into these spin moments of the PPT with opposite signs.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 68–71, May, 1976. 相似文献
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Wolfgang Köhler 《General Relativity and Gravitation》2011,43(6):1787-1825
A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation
of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace
Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads.
Matrix theory might solve a 27-year-old, fundamental problem of those theories (Sect. 4.1). For the standard test cases (PPN
scheme, Schwarz
schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions. 相似文献
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V. N. Tunyak 《Russian Physics Journal》1978,21(4):426-429
The tetrad theory of gravitation corresponding to the Treder formulation of the weak equivalence principle is incompatible with the customary method for constructing a gauge theory for a tetrad gravitational field. In this formulation, the Lagrangian of the nongravitating mass is a direct covariant generalization of the partially relativistic expression to a Riemannian space-time V4. This incompatibility is at odds with the resutt found in the tetrad formulation of the general theory of relativity derived from the requirement of localization of the Poincaré group.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 18–21, April, 1978. 相似文献
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微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论. 相似文献
11.
José W. Maluf 《Annalen der Physik》2013,525(5):339-357
A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group. 相似文献
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Arthur Komar 《Foundations of Physics》1985,15(4):473-485
The constraint formalism of classical mechanics is extended to field theories with gauge groups. Explicit examples of Klein-Gordon and Maxwell fields are presented. The symmetry properties of the Maxwell fields have the unexpcted feature in this formalism of forming a first-class algebra which is not Lie, a situation already encountered in the general theory of relativity. 相似文献
16.
Nathan Rosen 《Foundations of Physics》1985,15(10):997-1008
In the general relativity theory gravitational energy-momentum density is usually described by a pseudo-tensor with strange transformation properties so that one does not have localization of gravitational energy. It is proposed to set up a gravitational energy-momentum density tensor having a unique form in a given coordinate system by making use of a bimetric formalism. Two versions are considered: (1) a bimetric theory with a flat-space background metric which retains the physics of the general relativity theory and (2) one with a background corresponding to a space of constant curvature which introduces modifications into general relativity under certain conditions. The gravitational energy density in the case of the Schwarzschild solution is obtained. 相似文献
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R. F. Polishchuk 《Bulletin of the Lebedev Physics Institute》2013,40(10):275-281
Einstein-Cartan gravitational field equations are formed as Maxwell equations: the codifferential of the tetrad differential is equal to the conserved tetradic current. This yields local integral conservation laws for any tetrad field and, in particular, allows solving the old problem of the gravitational energy in the general relativity and Einstein-Cartan theories. 相似文献
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G.G.L. Nashed 《The European Physical Journal C - Particles and Fields》2007,51(2):377-383
Using a non-linear version of electrodynamics coupled to the teleparallel equivalent of general relativity (TEGR), we obtain
new regular exact solutions. The non-linear theory reduces to the Maxwell one in the weak limit with the tetrad fields corresponding
to a charged space-time. We then apply the energy-momentum tensor of the gravitational field, established in the Hamiltonian
structure of the TEGR, to the solutions obtained. 相似文献