Event Horizon Detecting Invariants

Abstract

Some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in $D>3$ dimensions, but they fail for the three dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here we provide an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces instead of the full spacetime. Our method is also applicable to black holes in generic dimensions but is most efficient in three, four, and five dimensions. We give four dimensional Kerr, five dimensional Myers-Perry and three dimensional warped-anti-de Sitter, and the three dimensional asymptotically flat black holes as examples.

arXiv comment5 pages, a simpler invariant is added for three dimensional metrics, reference added

References in corpus (10)

• The Black Hole in Three Dimensional Space Time
• Warped AdS_3 Black Holes
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• Curvature Invariants and Lower Dimensional Black Hole Horizons
• Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions
• Asymptotically flat black holes in 2+1 dimensions
• Cartan Invariants and Event Horizon Detection, Extended Version

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• New black hole solutions in three-dimensional $f(R)$ gravity
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Shedding Light on Gravity: Black Hole Shadows and Lensing Signatures in Lorentz Gauge Theory
• Scalar Curvature Invariants in Classical and Quantum Gravity