Abstract
Although it originated in the study of 4-dimensional spacetimes, the Newman-Penrose formalism is also an effective tool in dimension three, provided that a distinguished vector field is present. Here we show how a 3-dimensional version of the Newman-Penrose formalism can be used to study both the local and global geometry of Lorentzian 3-manifolds. Globally, we find obstructions to Lorentzian metrics generalizing those of constant curvature; locally, we classify Lorentzian 3-manifolds that admit a timelike Killing vector field. These results have appeared in [1] and [3], the latter joint with R. Ream.
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Aazami, A.B. (2022). Curvature and Killing Vector Fields on Lorentzian 3-Manifolds. In: Albujer, A.L., Caballero, M., GarcÃa-Parrado, A., Herrera, J., Rubio, R. (eds) Developments in Lorentzian Geometry. GELOMA 2021. Springer Proceedings in Mathematics & Statistics, vol 389. Springer, Cham. https://doi.org/10.1007/978-3-031-05379-5_4
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