Black hole lensing in Kerr-de Sitter spacetimes

TL;DR

This paper derives analytical solutions for photon orbits in Kerr-de Sitter spacetimes, enabling detailed ray-tracing and analysis of gravitational lensing effects, including higher-order images, which can test predictions of General Relativity.

Contribution

It provides the first analytical solutions for photon orbits in Kerr-de Sitter spacetimes and applies them to ray-tracing and lensing analysis, enhancing understanding of black hole imaging.

Findings

Higher-order images closely resemble the critical curve.

Analytical solutions for photon ring parameters were obtained.

Higher-order images are promising for testing General Relativity.

Abstract

We have derived analytical solutions using Jacobi elliptic functions for bound and nearly bound photon orbits in Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) spacetimes. Leveraging our obtained solutions, we have conducted an analytic ray-tracing in both spacetimes. We have obtained direct images, lensing rings and photon rings for equatorial disks considering inclined locally static observers. Images corresponding to n=(2,3) exhibit a significantly closer resemblance to the critical curve as compared to the n=1 image. This highlights the remarkable potential of these higher-order images as robust testing grounds for General Relativity (GR). Furthermore in both spacetimes, we have obtained analytical solutions for the critical parameters governing the structure of the photon ring and analyzed these parameters in details.