A spacetime not characterised by its invariants is of aligned type II
General Relativity and Quantum Cosmology
2015-05-30 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of type II. This implies, using the boost-weight decomposition, that for such a metric there exists a frame such that all positive boost-weight components are zero. Indeed, we show a more general result, namely that any set of tensors which is not characterised by its invariants, must be of aligned type II. This result enables us to prove a number of related results, among them the algebraic VSI conjecture.
Keywords
Cite
@article{arxiv.1109.2551,
title = {A spacetime not characterised by its invariants is of aligned type II},
author = {Sigbjorn Hervik},
journal= {arXiv preprint arXiv:1109.2551},
year = {2015}
}
Comments
14pages, CQG to appear