Signatures of the Israel Junction II: Double Photon Rings in Slowly Rotating Kerr Spacetime with Thin Shell

TL;DR

This paper investigates how a thin shell in a slowly rotating Kerr spacetime affects photon trajectories and images, revealing unique features like double photon rings and step-like structures that could inform astrophysical observations.

Contribution

It introduces a novel analysis of photon behavior across a thin shell in Kerr spacetime, highlighting distinctive image features and their potential observational implications.

Findings

Double photon rings observed in the images.

Photon rings can merge into a single ring.

Shadow boundaries do not directly correspond to photon rings.

Abstract

Applying the junction conditions to the slowly rotating Kerr spacetime with a thin shell, we find that while the angular momentum $L$ and Carter constant $C$ of the ray remain unchanged upon crossing the shell, its energy $E$ does not. Consequently, the impact parameters $\eta=L/E$ and $\xi=C/E^2$ of the ray are discontinued at the shell. Utilizing this transformation, we study the shadow of this spacetime and the corresponding images from an equatorial thin accretion disk. The presence of the shell gives rise to distinctive features in the observed images. Notably, we observe distinct double photon rings in the images, which can gradually merge into a single ring. Moreover, the shadow boundaries and the photon rings do not exhibit a one-to-one correspondence. The abrupt changes in redshift factor and the truncated photon regions profoundly influence the image, producing distinctive features such as the step-like structures. These features in shell-equipped spacetimes can help evaluate, through future astronomical observations, the applicability of the Israel junction condition and the shell model in real astrophysical systems.