Petrov Types for the Weyl Tensor via the Riemannian-to-Lorentzian Bridge

Autor:	Aazami, Amir Babak
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	We analyze oriented Riemannian 4-manifolds whose Weyl tensors $W$ satisfy the conformally invariant condition $W(T,\cdot,\cdot,T) = 0$ for some nonzero vector $T$. While this can be algebraically classified via $W$'s normal form, we find a further geometric classification by deforming the metric into a Lorentzian one via $T$. We show that such a $W$ will have the analogue of Petrov Types from general relativity, that only Types I and D can occur, and that each is completely determined by the number of critical points of $W$'s associated Lorentzian quadratic form. A similar result holds for the Lorentzian version of this question, with $T$ timelike. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.20915 Zobrazit plný text záznamu View this record from Arxiv