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arXiv · 2405.20246

Detecting horizons of symmetric black holes using relative differential invariants

David McNutt·Eivind Schneider
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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.

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David McNutt, Eivind Schneider. 2024-05-30. Detecting horizons of symmetric black holes using relative differential invariants. https://arxiv.org/abs/2405.20246

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