Boomerang photons around spherically symmetric black holes

Abstract

The gravitational field of celestial bodies can be strong enough to deflect photons or even trap photons at the photon sphere. This paper is a study of boomerang photons in the spacetimes of spherically symmetric black holes. These are photons that start at some position, go around a black hole, and return to its starting point. The motion of a massless particle is completely specified by its impact parameter b which is just the ratio of its conserved angular momentum and energy. The impact parameter can be adjusted to obtain a photon orbit making $n$ revolutions about a black hole for boomerang orbits. We numerically compute impact parameter spectra, discrete sets of impact parameters {b₁; b₂; : : : ; b_n; : : : ; b_∞} for boomerang orbits, bounded by a critical impact parameter, b_∞, which corresponds to a trapped photon orbit. The spectrum is sensitive to black hole parameters: it expands as the photon is emitted further from the Schwarzschild black hole; shrinks as its charge Q increases; expands when we positively increase the cosmological constant Λ of a (anti-)de Sitter universe; and shrinks as we consider higher spacetime dimensions. Boomerang photons may potentially find use in the pursuit of fuel-free interstellar travel such as a halo drive.