Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Equivalence of the Regge and Einstein equations using Cartan's moment of rotation

Abstract

An explicit derivation of the Einstein tensor via Cartan's moment of rotation on an infinitesimal lattice is presented. With the standard form of the Einstein equations assumed, the equivalence of the Regge equations with matter to the Einstein equations is demonstrated in detail using a spherically symmetric example with proper time slicing. Such an example has been numerically evolved to withinr=2M using null struts. These results make Regge calculus more readily applicable and provide a justification for its use.

This is a preview of subscription content, log in to check access.

References

  1. Adler, Ronald,et al. (1975).Introduction to General Relativity, 2nd ed., McGraw-Hill, New York, p. 277.

  2. Helgason, Sigurdur (1962).Differential Geometry and Symmetric Spaces. Academic Press, New York, p. 19.

  3. Kemmell, Bruce M. (1992). Null-strut Regge calculus: Spherically symmetric stellar collapse, Ph.D. dissertation, University of New Mexico.

  4. Kheyfets, Arkady (1986). Austerity and geometric structure of field theories, Ph.D. dissertation, University of Texas at Austin.

  5. Kheyfets, Arkady,et al. (1990).Physical Review D,41(12), 3637.

  6. Kheyfets, Arkady, and Miller, Warner A. (1991).Journal of Mathematical Physics,32(11), 3168.

  7. Kheyfets, Arkady, and Miller, Warner A. (1992).Journal of Mathematical Physics,33(6), 2242.

  8. Lovelock, David, and Rund, Hanno (1975).Tensor Calculus, Differential Forms, and Variational Principles, Wiley, New York, p. 343.

  9. Misner, C., Thorne, K., and Wheeler, J. (1973).Gravitation, Freeman, San Francisco, p. 375.

  10. Regge, Tullio (1961).Nuovo Cimento,XIX(3), 558.

  11. Straumann, Norbert (1984).Relativistic Astrophysics, Springer-Verlag, Berlin, p. 37.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kemmell, B.M. Equivalence of the Regge and Einstein equations using Cartan's moment of rotation. Int J Theor Phys 33, 1699–1709 (1994). https://doi.org/10.1007/BF00672694

Download citation

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Standard Form
  • Einstein Equation