Dimension of the isometry group in type N vacuum solutions: an IDEAL approach

Fuente: arXiv
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Main Authors: Sáez, Juan Antonio, Mengual, Salvador, Ferrando, Joan Josep
Format: Preprint
Published: 2025
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author Sáez, Juan Antonio
Mengual, Salvador
Ferrando, Joan Josep
author_facet Sáez, Juan Antonio
Mengual, Salvador
Ferrando, Joan Josep
contents The necessary and sufficient conditions for a type N vacuum solution (with cosmological constant) to admit a group of isometries of dimension $r$ are given in terms of the invariant concomitants of the Weyl tensor. This study requires defining several invariant classes, and for each class, the conditions that determine the dimension are given. Thus, an IDEAL (Intrinsic, Deductive, Explicit and ALgorithmic) characterisation of these spacetimes follows. Some examples show that our algorithmic results can easily be implemented on the \textit{xAct Mathematica} suite of packages. The relation between our classes and already known families of solutions of Einstein equations is outlined.
format Preprint
id arxiv_https___arxiv_org_abs_2506_20427
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Dimension of the isometry group in type N vacuum solutions: an IDEAL approach
Sáez, Juan Antonio
Mengual, Salvador
Ferrando, Joan Josep
General Relativity and Quantum Cosmology
The necessary and sufficient conditions for a type N vacuum solution (with cosmological constant) to admit a group of isometries of dimension $r$ are given in terms of the invariant concomitants of the Weyl tensor. This study requires defining several invariant classes, and for each class, the conditions that determine the dimension are given. Thus, an IDEAL (Intrinsic, Deductive, Explicit and ALgorithmic) characterisation of these spacetimes follows. Some examples show that our algorithmic results can easily be implemented on the \textit{xAct Mathematica} suite of packages. The relation between our classes and already known families of solutions of Einstein equations is outlined.
title Dimension of the isometry group in type N vacuum solutions: an IDEAL approach
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2506.20427