Symmetries in Riemann-Cartan Geometries

被引:0
|
作者
Mcnutt, David D. [1 ]
Coley, Alan A. [2 ]
Van Den Hoogen, Robert J. [3 ]
机构
[1] Polish Acad Sci, Ctr Theoret Phys, Warsaw, Poland
[2] Dalhousie Univ, Dept Math & Stat, Halifax, NS, Canada
[3] St Francis Xavier Univ, Dept Math & Stat, Antigonish, NS, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
symmetry; Riemann-Cartan; frame formalism; local homogeneity; TORSION THEORIES;
D O I
10.3842/SIGMA.2024.078
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries. One notable difference, is the number of symmetries for a Riemann-Cartan geometry is potentially smaller than the number of Killing vector fields for the metric. In this paper, we will review the investigation of symmetries in Riemann-Cartan geometries and the mathematical tools used to determine geometries that admit a given group of symmetries. As an illustration, we present new results by determining all static spherically symmetric and all stationary spherically symmetric Riemann-Cartan geometries. Furthermore, we have determined the subclasses of spherically symmetric Riemann-Cartan geometries that admit a seven-dimensional group of symmetries.
引用
收藏
页数:20
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