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Annali di Matematica Pura ed Applicata

, Volume 53, Issue 1, pp 21–39 | Cite as

Einstein-maxwell fields in the presence of matter and pressure

  • Václav Hlavatý
Article

Summary

Given the gravitational field hλμ one has to find the electromagnetic tensor field kλμ concomitant of hλμ which is not of the third class and which satisfies the conditions
$$R_{\mu \lambda } - Rh_{\mu \lambda } /2 = \mu u_\mu u_\lambda - F_{\mu \lambda } + ph_{\mu \lambda } $$
(a))
$$\partial _{\left[ {\omega k\mu \lambda } \right]} = 0$$
(b))
$$\nabla \alpha k\alpha \nu = \in u_\nu $$
(c))
where uv is a unit vector. Necessary and sufficient conditions for the solution of this problem will be given. If they are satisfied then the concomitants of hλμ
$$k_{\lambda \mu ,u\lambda ,\mu ,} \varepsilon $$
can be obtained bypurely algebraic operations, while the concomitant p of hλμ satisfies also the differential equation
$$u^\lambda \partial _\lambda p = 0.$$
The actual construction of all concomitants will be given.

Keywords

Differential Equation Unit Vector Gravitational Field Tensor Field Actual Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [1]
    G. Y. Rainich,Electrodynamics in the general relativity theory, « Trans. Am. Math. Soc. », 27 (1925) p. 106.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    Ch. W. Misner - J. A. Wheeler,Geometrodynamics, « Am Phys., 2 » (1957), p. 525.Google Scholar
  3. [3]
    V. Hlavatý,Geometry of Einstein's Unified Field Theory, P. Noordhoff, Groningen, (1958), pp. 341Google Scholar
  4. [4]
    V. Hlavatý,Einstein-Maxwell fields. « Journal de Math. », Volume dedicated to R. Garnier. In print.Google Scholar
  5. [5]
    V. Hlavatý,Rigid motion in a Riemann space, I, « Circolo Mat. di Palermo ». In print.Google Scholar
  6. [6]
    V. Hlavatý,Rigid motion in a Riemann space, II, « Circolo Mat. di Palermo », In print.Google Scholar

Copyright information

© Swets & Zeitlinger B. V. 1961

Authors and Affiliations

  • Václav Hlavatý
    • 1
  1. 1.BloomingtonU. S. A.

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