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.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Adler, Ronald,et al. (1975).Introduction to General Relativity, 2nd ed., McGraw-Hill, New York, p. 277.
Helgason, Sigurdur (1962).Differential Geometry and Symmetric Spaces. Academic Press, New York, p. 19.
Kemmell, Bruce M. (1992). Null-strut Regge calculus: Spherically symmetric stellar collapse, Ph.D. dissertation, University of New Mexico.
Kheyfets, Arkady (1986). Austerity and geometric structure of field theories, Ph.D. dissertation, University of Texas at Austin.
Kheyfets, Arkady,et al. (1990).Physical Review D,41(12), 3637.
Kheyfets, Arkady, and Miller, Warner A. (1991).Journal of Mathematical Physics,32(11), 3168.
Kheyfets, Arkady, and Miller, Warner A. (1992).Journal of Mathematical Physics,33(6), 2242.
Lovelock, David, and Rund, Hanno (1975).Tensor Calculus, Differential Forms, and Variational Principles, Wiley, New York, p. 343.
Misner, C., Thorne, K., and Wheeler, J. (1973).Gravitation, Freeman, San Francisco, p. 375.
Regge, Tullio (1961).Nuovo Cimento,XIX(3), 558.
Straumann, Norbert (1984).Relativistic Astrophysics, Springer-Verlag, Berlin, p. 37.
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
- Field Theory
- Elementary Particle
- Quantum Field Theory
- Standard Form
- Einstein Equation