Projective structure and holonomy in general relativity

G S Hall (1) , D P Lonie (2)

1 Institute of Mathematics
2 School of Computing

This paper presents a study of the situation when two space-times admit the same (unparametrised) geodesics, that is, when they are projectively related. The solution is based on the curvature class and the holonomy type of a space-time and it transpires that all holonomy possibilities can be solved except the most general one and that the consequence of two space-times being projectively related leads, in many cases, to their associated Levi-Civita connections being identical. Some results are also given regarding the general case. It is also shown that the holonomy types of projectively related space-times are very closely related. The theory is then applied, with Einsteins principle of equivalence in mind, to " generic " space-times.

Mots clés: 04.20.-q; 02.40.-k; 02.40.Ky

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

G S Hall, D P Lonie. Projective structure and holonomy in general relativity. Classical and Quantum Gravity, 2011, 28 (8), pp.83101. ⟨10.1088/0264-9381/28/8/083101⟩. ⟨hal-00690071⟩