Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

Details Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

2001-02-07

arxiv.org/abs/gr-qc/0102028v4

Commun.Theor.Phys. 37 (2002) 11-14

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex 7 pages; no figures. Significant modifications being given, with references added

Scientific paper

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such solutions can be expressed with Chebyshev's polynomials.

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