Specialized computer algebra system for application in general relativity
A brief characteristic of the specialized computer algebra system GRG_EC intended for symbolic computations in the field of general relativity is given.
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arXiv subjects
S. Tertychniy
Publications and source records attributed to S. Tertychniy.
On the alternative description of complex holomorphic and Lorentz geometries in four dimensions
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is spread to the metric case in terms of notion of normalized ordered oriented transection field. As a result, one obtains a possibility to handle the metric geometry without any references to the metric tensor itself on a distinct base which nevertheless contains all the information on metricity. Moreover, the notion of space-time curvature is provided with its natural counterpart in the transection `language' in a form of curvature endomorphism as well. To globalize the local constructions introduced, a certain fiber bundle is defined whose sections are equivalent to normalized ordered oriented transection fields and locally to the metric tensor on space-time. The criterion distinguishing the Lorentz geometry is discussed. The resulting alternative method of the description of space-time metricity, dealing with exterior forms foliation alone, seems to be of a power compatible with one of the standard concept based on the metric tensor.
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On the alternative description of complex holomorphic and Lorentz geometries in four dimensions. II. Appendix
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
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Application of the Lagrange-Souriau form method to the case of source-free electromagnetic field
The recent method of the description of classical fields in terms of Lagrange-Souriau form is applied to the case of source-free electromagnetic field in order to check its computational capabilities. The relevant calculations are represented in all details and yield a useful data for comparisons of the method with more usual approaches in this simple and transparent case.
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On the principles of description of time and space relationships in frames of general relativity
The problem of the referring of space and time relationships between physical objects in a curved space-time is discussed. The basic notions of column and weak column that could constitute the basis for consistent general relativistic description of measurements of space and time relations are introduced and the corresponding equations are derived. A column of observers is proposed to realize still vague notion of `non-inertial frame of reference' in case of curved space-time, the criterion distinguishing `inertial columns' is suggested as well. A number of solutions of column equations is described. They are applied for calculation of gravitational, inertial (or gravitational-inertial in more general situation) and ``external" forces and the strength of gravitational field in several cases of physical interest. In particular, the `general relativistic' version of Newton's law of inverse squares is derived in case of the interaction of test particle with a static central symmetric body.
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Local Determination of the Light Deflection in the Sperically Symmetric Static Gravitational Field
The new method of invariant definition of the measurable angle of light deflection in the static central symmetric gravitational field is suggested. The predicted pure gravitational contribution to the deflection angle slightly differs from its classical estimate and one may hope that this discrepancy could be experimentally detected in the near future. (uuencoded,compressed PostScript, 23 p. inc. 2 fig.)
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