Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry
General Relativity and Quantum Cosmology
2018-01-17 v4 High Energy Physics - Lattice
High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.gr-qc/0102028,
title = {Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry},
author = {Jian Dai and Xing-Chang Song},
journal= {arXiv preprint arXiv:gr-qc/0102028},
year = {2018}
}
Comments
Latex 7 pages; no figures. Significant modifications being given, with references added