2021/07/01 by Albert Sneppen · 1 citation
Mathematics · Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Black hole (networking) #Charged black hole #Classical mechanics #Computer science #Entropy (arrow of time) #Event (particle physics) #Event horizon #Experimental and Theoretical Physics Studies #Exponential function #Extremal black hole #General relativity #Geodesic #Geometry #Gravitation #Logarithm #Mathematical analysis #Mathematics #Photon #Photon sphere #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Quasinormal mode #Relativity and Gravitational Theory #Rotating black hole #Schwarzschild metric #Schwarzschild radius #Theoretical physics
paper · pdf · doi:10.1038/s41598-021-93595-w
openalex publication_date 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor [Formula: see text] closer to the black hole's optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.