Detecting horizons of symmetric black holes using relative differential invariants

2024/05/30 by McNutt, David, Schneider, Eivind · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2405.20246

Abstract

Let \mathfrakk 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 \mathfrakk. We show that scalar relative differential invariants, with respect to a Lie algebra of vector fields on M preserving \mathfrakk, can be used to detect the horizons of several well-known black holes. In particular, using the Lie algebra structure of \mathfrakk, we construct a general relative differential invariant of order 0 that always vanishes on \mathfrakk-invariant Killing horizons.

Cited by

• Where are linearized gauge invariants encoded for plane waves in linearized gravity?

Related

• Detecting Event Horizons and Stationary Surfaces
• Near-Horizon Symmetries of Local Black Holes in General Relativity
• Cartan Invariants and Event Horizon Detection, Extended Version
• Differential curvature invariants and event horizon detection for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime
• All superalgebras for warped AdS₂ and black hole near horizon geometries