Detecting horizons of symmetric black holes using relative differential invariants
Abstract
Let $\mathfrak{k}$ 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 $\mathfrak{k}$. We show that scalar relative differential invariants, with respect to a Lie algebra of vector fields on M preserving $\mathfrak{k}$, can be used to detect the horizons of several well-known black holes. In particular, using the Lie algebra structure of $\mathfrak{k}$, we construct a general relative differential invariant of order 0 that always vanishes on $\mathfrak{k}$-invariant Killing horizons.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.20246
- arXiv:
- arXiv:2405.20246
- Bibcode:
- 2024arXiv240520246M
- Keywords:
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- General Relativity and Quantum Cosmology;
- Mathematics - Differential Geometry
- E-Print:
- 29+3 pages