| 研究実績の概要 |
We have addressed the problem of algebraic classification in Weyl-Cartan geometry and obtained all the possible algebraic types of the irreducible parts of the curvature tensor. In particular, we have shown that the curvature tensor can be decomposed in general metric-affine geometries into 11 fundamental parts, which include both Riemannian and post-Riemannian quantities with torsion and nonmetricity. In particular, it is demonstrated that the standard type D algebraic structure associated with black holes endowed with abelian interactions, such as the Kerr-Newman solution of General Relativity that describes a rotating charged black hole, cannot occur in the presence of the spin-orbit interaction of the Metric-Affine Gravity model under consideration. Therefore, the main conclusion is that the spin-orbit interaction modifies the geometry of the space-time, preventing such a specially algebraic type for a more general one, which gives rise to a more complicated system of nonlinear differential equations yet to be solved. This work has already been reviewed and published in Physical Review D.
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