Year: 2025
Type: article
Abstract: Let k be a nontrivial finite-dimensional Lie algebra of vector fields on a manifold M, and consider the family of Lorentzian metrics on M whose Killing algebra contains k . We show that scalar relative differential invariants of such metrics, with respect to a Lie algebra of vector fields on M preserving k , can be used to detect the horizons of several well-known black holes. In particular, using the Lie algebra structure of k , we construct a general relative differential invariant of order 0 that always vanishes on k -invariant Killing horizons. While the current work is meant to demonstrate the relevance of jet bundles and relative differential invariants in physical applications, we also provide a computationally simple approach for finding a relative differential invariant that detects Killing horizons. The computation and use of this relative differential invariant is comparable in difficulty to other horizon detection methods when there is an obvious Killing vector field that generates the Killing horizon, and often simpler when the preferred Killing vector field is not obvious.
Source: Classical and Quantum Gravity
Authors: David McNutt, Eivind Schneider
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Funder: Tromsø Forskningsstiftelse
OpenAlex ID: W4409423446