Image formation in weak gravitational lensing by tidal charged black holes

TL;DR

This paper develops a weak lensing model for tidal charged black holes, highlighting differences from Schwarzschild black holes, especially in flux ratios and brightness relations, which could help identify spacetime structures.

Contribution

It introduces a generic weak lensing equation for tidal charged black holes and compares their lensing signatures to Schwarzschild black holes at various orders.

Findings

Flux ratio modifications are significant in tidal charged black holes.

Image brightness ratios follow a distinct power-law relation.

Number and orientation of images resemble Schwarzschild lensing when tidal charge dominates.

Abstract

We derive a generic weak lensing equation and apply it for the study of images produced by tidal charged brane black holes. We discuss the similarities and point out the differences with respect to the Schwarzschild black hole weak lensing, to both first and second order accuracy, when either the mass or the tidal charge dominates. In the case of mass dominated weak lensing, we analyze the position of the images, the magnification factors and the flux ratio, as compared to the Schwarzschild lensing. The most striking modification appears in the flux ratio. When the tidal charge represents the dominating lensing effect, the number and orientation of the images with respect to the optical axis resembles the lensing properties of a Schwarzschild geometry, where the sign associated with the mass is opposite to that for the tidal charge. Finally it is found that the ratio of the brightness of images as a function of image separation in the case of tidal charged black holes obeys a power-law relation significantly different from that for Schwarzschild black holes. This might provide a means for determining the underlying spacetime structure.