Working Paper 28
Sensitive Light: Geometry, Chaos, and Information Recovery in Null Transport
October 2026
Abstract
How sensitively does light propagation depend on initial conditions, how far ahead can it be predicted, and how much information about the source survives in partial observations? This paper measures all three across geometries and media, keeping four regimes distinct: stable, unstable but non-chaotic, chaotic, and predictably reconstructable. For unstable photon orbits the organizing quantity is the ratio of the coordinate-time Lyapunov exponent to the orbital frequency, λt/Ωc: it equals 1 for Schwarzschild and for the Ellis wormhole throat (whose exponent we compute in closed form, λt = 1/a), collapses to 0.134 for near-extremal prograde Kerr, and equals √(d−3) for Tangherlini black holes (proved here). Scattering measurements confirm the framework: the winding-number divergence near the critical impact parameter fits the predicted coefficient 1/(2π) to 0.3%, and the arrival-time sensitivity per winding grows with slope 6.323 against the analytic 2π. The Majumdar–Papapetrou di-hole, the one genuinely chaotic spacetime computed, has a fractal exit-basin boundary confined to a thin set (uncertainty exponent α = 0.669, boundary dimension 0.33 on a one-dimensional cut, first such measurement for this system), no long-lived rays in ~51,000 integrated rays (so no escape rate is measurable at these parameters), and outcome statistics that remain 99.3% recoverable under coarse-graining at resolution 10−2. A double plasma lens is, by contrast, regular (α = 1.01) and remains regular across a strong-coupling scan, and its angular focus desynchronizes arrival times by a factor of 54. On information recovery the paper separates conditional from expected Fisher information and states the resulting chaos–information tradeoff as a conjecture with three named cutoffs (wave optics, finite source size, dwell time), against the control case of an integrable point lens whose Cramér–Rao bound saturates at the caustic.
Keywords
null geodesics, Lyapunov exponents, chaotic scattering, black holes, wormholes, gravitational lensing, plasma lenses, Fisher information, predictability