2008/08/07 by V. M. Khatsymovsky, Khatsymovsky, V. M.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0808.1041
9 pages
arxiv created 2008/08/07 · openalex publication_date 2008/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider simplest piecewise flat manifold consisting of two identical 4-tetrahedra (call it bisimplex). General relativity action for arbitrary piecewise flat manifold can be expressed in terms of sum of the (half of) bisimplex actions. We use representation of each bisimplex action in terms of certain rotation matrices (connections). This gives representation of any minisuperspace piecewise flat gravity system in terms of connections which do not connect neighboring 4-tetrahedra (more appropriate would be call these self-connections). If Regge calculus with independent 4-tetrahedra is considered, i. e. when the length of an edge is not constrained to be the same for all the 4-tetrahedra containing this edge, self-connection representation leaves 4-tetrahedra independent also in connection matrices sector. Action remains sum of independent 4-tetrahedra terms.