Universal properties of the near-horizon optical geometry

Abstract

We make use of the fact that the optical geometry near a static non-degenerate Killing horizon is asymptotically hyperbolic to investigate universal features of black hole physics. We show how the Gauss-Bonnet theorem allows certain lensing scenarios to be ruled in or out. We find rates for the loss of scalar, vector and fermionic `hair' as objects fall quasi- statically towards the horizon. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending the flat space result of Feinberg and Sucher. We use the enhanced conformal symmetry of the Schwarzschild and Reissner-Nordstrom backgrounds to re-derive the electrostatic field due to a point charge in a simple fashion.

References in corpus (4)

• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Quantum Theory on Lobatchevski Spaces
• The Geometry of Large Causal Diamonds and the No Hair Property of Asymptotically de-Sitter Spacetimes
• Green functions and dimensional reduction of quantum fields on product manifolds

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• Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo
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• The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis
• A General Discussion on Photon Spheres in Different Categories of Spacetimes
• Kiselev-inspired Wormholes
• On Effective Dimensional Reduction in Hyperbolic Spaces
• Optical Metrics and Projective Equivalence
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Investigating Graviton Mass Effects on Black Hole Lensing in dRGT Massive Gravity
• Asymptotically flat anisotropic space-time in 5 dimensions