Simplicial lattices in classical and quantum gravity: Mathematical structure and application

Miscellaneous · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5928910

LaFave, N J

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The author develops the mathematics of simplicial lattices to the same level of sophistication as the mathematics of pseudo-Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. He applies this mathematical formalism to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC, developed by Warner Miller, describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. The outstanding problems discussed include (a) the rigidification of the 3-layered sandwich and the evolution problem; (b) the formulation of initial data; and (c) in inclusion of matter on the lattice. The resulting calculational scheme is applied to two test problems, the Friedmann model and the second-order Doppler effect. Finally, he describes avenues of investigation for NSC in quantum gravity.

• Research Organization: Texas Univ., Austin, TX (USA)
• OSTI ID: 5928910
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GENERAL RELATIVITY THEORY
MATHEMATICS
QUANTUM GRAVITY
CALCULATION METHODS
DIFFERENTIAL GEOMETRY
GEOMETRY
MATHEMATICAL MANIFOLDS
REGGE CALCULUS
SPACE-TIME
SPINORS
TENSORS
TOPOLOGY
FIELD THEORIES
QUANTUM FIELD THEORY
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