Relativistic Images in Randall-Sundrum II Braneworld Lensing

TL;DR

This paper investigates gravitational lensing by black holes in the Randall-Sundrum II braneworld, revealing significant differences in image magnifications due to tidal charge effects and validating approximation methods for bending angles.

Contribution

It introduces a new parameterization of tidal charge in the TRN metric, showing enhanced lensing effects for braneworld black holes, and provides a mathematical validation of the bending angle approximation.

Findings

Tidal charge significantly increases image magnifications for primordial black holes.

The new parameterization improves understanding of lensing in braneworld scenarios.

The logarithmic bending angle approximation is valid across all tidal charges.

Abstract

In this paper, we explore the properties of gravitational lensing by black holes in the Randall-Sundrum II braneworld. We use numerical techniques to calculate lensing observables using the Tidal Reissner-Nordstrom (TRN) and Garriga-Tanaka metrics to examine supermassive black holes and primordial black holes. We introduce a new way tp parameterize tidal charge in the TRN metric which results in a large increase in image magnifications for braneworld primordial black holes compared to their 4 dimensional analogues. Finally, we offer a mathematical analysis that allows us to analyze the validity of the logarithmic approximation of the bending angle for any static, spherically symmetric metric. We apply this to the TRN metric and show that it is valid for any amount of tidal charge.