The symplectic geometry of the black hole photon shell

Fuente: arXiv
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Autores principales: Shir, Judy, Hadar, Shahar
Formato: Preprint
Publicado: 2025
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author Shir, Judy
Hadar, Shahar
author_facet Shir, Judy
Hadar, Shahar
contents The unstably bound, critical null geodesics of the Kerr spacetime form a distinguished class of orbits whose properties govern observables such as the photon ring and the high-frequency component of black-hole ringdown. This set of orbits defines a codimension-two submanifold of the null-geodesic phase space known as the photon shell. In this work we investigate the photon shell's intrinsic symplectic geometry. Using the induced symplectic form, we construct the canonical volume form on the shell and compute the differential phase-space volume it encloses as a function of radius -- equivalently, the radial density of states. In the near-extremal limit the photon shell bifurcates into near-horizon and far-region components; we find that approximately $3\%$ of the shell's phase-space volume resides in the near-horizon component. We also analyze a thickening of the photon shell that includes near-critical orbits, and compute its differential phase-space volume. Beyond their intrinsic theoretical interest, these results may inform the interpretation of high-resolution observations of spinning black holes.
format Preprint
id arxiv_https___arxiv_org_abs_2510_23753
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The symplectic geometry of the black hole photon shell
Shir, Judy
Hadar, Shahar
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
High Energy Physics - Theory
The unstably bound, critical null geodesics of the Kerr spacetime form a distinguished class of orbits whose properties govern observables such as the photon ring and the high-frequency component of black-hole ringdown. This set of orbits defines a codimension-two submanifold of the null-geodesic phase space known as the photon shell. In this work we investigate the photon shell's intrinsic symplectic geometry. Using the induced symplectic form, we construct the canonical volume form on the shell and compute the differential phase-space volume it encloses as a function of radius -- equivalently, the radial density of states. In the near-extremal limit the photon shell bifurcates into near-horizon and far-region components; we find that approximately $3\%$ of the shell's phase-space volume resides in the near-horizon component. We also analyze a thickening of the photon shell that includes near-critical orbits, and compute its differential phase-space volume. Beyond their intrinsic theoretical interest, these results may inform the interpretation of high-resolution observations of spinning black holes.
title The symplectic geometry of the black hole photon shell
topic General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
High Energy Physics - Theory
url https://arxiv.org/abs/2510.23753