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The mean curvature of gravitational fields

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  • Marathe, Kishore B.

Abstract

The mean curvature of a gravitational field is defined as a generalization of the average curvature in a given direction by using the gravitational sectional curvature function on non-degenerate tangent 2-planes to the space-time manifold. We find that the mean curvature of a gravitational field is independent of direction as determined by a unit vector. The converse of this result provides a new characterization of spaces admitting gravitational fields. We also define the average curvature (or bending) of a non-degenerate k-plane in a gravitational field and show that it is independent of the choice of non-degenerate k-plane.

Suggested Citation

  • Marathe, Kishore B., 1982. "The mean curvature of gravitational fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 143-145.
    • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:143-145
    DOI: 10.1016/0378-4371(82)90274-6
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