Null-strut calculus. I. Kinematics

Arkady Kheyfets; Norman J. LaFave; Warner A. Miller

doi:10.1103/PhysRevD.41.3628

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Null-strut calculus. I. Kinematics

Arkady Kheyfets^*, Norman J. LaFave, and Warner A. Miller

Spacetime Physics Group, High Energy Plasma Division, Weapons Laboratory, Kirtland Air Force Base, Albuquerque, New Mexico 87117-6008

^*Permanent address: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205.

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Phys. Rev. D 41, 3628 – Published 15 June, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.3628

Abstract

This paper describes the kinematics of null-strut calculus—a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to "earlier" and "later" momentumlike lattice surfaces (TET*) entirely by light rays or "null struts." These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity.

References (21)

T. Regge, Nuovo Cimento 19, 558 (1961)
C. Y. Wong, J. Math. Phys. 12, 70 (1971)
P. A. Collins and R. M. Williams, Phys. Rev. D 5, 1908 (1972)
P. A. Collins and R. M. Williams, Phys. Rev. D 7, 965 (1973)
P. A. Collins and R. M. Williams, Phys. Rev. D 10, 3537 (1974)
J. Porter, Class. Quantum Grav. 4, 391 (1987)
J. Porter, Class. Quantum Grav. 4, 375 (1987)
L. Brewin, Class. Quantum Grav. 5, 839 (1988)
A. Kheyfets, N. J. LaFave, and W. A. Miller, J. Math. Phys. (to be published)
A. Kheyfets, N. J. LaFave, and W. A. Miller, Phys. Rev. D 39, 1097 (1988)
N. J. LaFave, Dissertation, The University of Texas at Austin, 1989
J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1966)
A. Kheyfets, N. J. LaFave, and W. A. Miller, Class. Quantum Grav. 6, 659 (1989)
H. S. M. Coxeter, Regular Polytopes (Dover, New York, 1973)
G. Grünbaum, Convex Polytopes (Interscience, New York, 1967)
L. Fejes Tóth, Regular Figures (Macmillan-Pergamon, New York, 1964)
A. Brondsted, An Introduction to Convex Polytopes (Springer, New York, 1983)
J. A. Wheeler, in Relativity, Groups, and Topology, edited by C. DeWitt and B. DeWitt (Gordon and Breach, New York, 1964), p. 463
A. Kheyfets, N. J. LaFave, and W. A. Miller, following paper, Phys. Rev. D 41, 3637 (1990)
W. A. Miller, Dissertation, The University of Texas of Austin, 1986
J. R. Munkres, Elementary Differential Topology (Princeton University Press, Princeton, NJ, 1963), p. 65

[c1] T. Regge, Nuovo Cimento 19, 558 (1961)

[c2] C. Y. Wong, J. Math. Phys. 12, 70 (1971)

[c3] P. A. Collins and R. M. Williams, Phys. Rev. D 5, 1908 (1972)

[c4] P. A. Collins and R. M. Williams, Phys. Rev. D 7, 965 (1973)

[c5] P. A. Collins and R. M. Williams, Phys. Rev. D 10, 3537 (1974)

[c6] J. Porter, Class. Quantum Grav. 4, 391 (1987)

[c7] J. Porter, Class. Quantum Grav. 4, 375 (1987)

[c8] L. Brewin, Class. Quantum Grav. 5, 839 (1988)

[c9] A. Kheyfets, N. J. LaFave, and W. A. Miller, J. Math. Phys. (to be published)

[c10] A. Kheyfets, N. J. LaFave, and W. A. Miller, Phys. Rev. D 39, 1097 (1988)

[c11] N. J. LaFave, Dissertation, The University of Texas at Austin, 1989

[c12] J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1966)

[c13] A. Kheyfets, N. J. LaFave, and W. A. Miller, Class. Quantum Grav. 6, 659 (1989)

[c14] H. S. M. Coxeter, Regular Polytopes (Dover, New York, 1973)

[c15] G. Grünbaum, Convex Polytopes (Interscience, New York, 1967)

[c16] L. Fejes Tóth, Regular Figures (Macmillan-Pergamon, New York, 1964)

[c17] A. Brondsted, An Introduction to Convex Polytopes (Springer, New York, 1983)

[c18] J. A. Wheeler, in Relativity, Groups, and Topology, edited by C. DeWitt and B. DeWitt (Gordon and Breach, New York, 1964), p. 463

[c19] A. Kheyfets, N. J. LaFave, and W. A. Miller, following paper, Phys. Rev. D 41, 3637 (1990)

[c20] W. A. Miller, Dissertation, The University of Texas of Austin, 1986

[c21] J. R. Munkres, Elementary Differential Topology (Princeton University Press, Princeton, NJ, 1963), p. 65

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Null-strut calculus. I. Kinematics

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Null-strut calculus. II. Dynamics

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