Universal properties of the near-horizon optical geometry

TL;DR

This paper explores universal features of black hole near-horizon geometries using hyperbolic space properties, revealing insights into lensing, hair loss rates, and electromagnetic interactions near horizons.

Contribution

It introduces a novel approach leveraging hyperbolic geometry and conformal symmetry to analyze black hole near-horizon physics and derive new results.

Findings

Lens scenarios constrained by Gauss-Bonnet theorem

Rates of hair loss for scalar, vector, and fermionic fields

Extended Lienard-Wiechert potential and electron-neutrino force calculation

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.