Measuring black hole spin through gravitational lensing of pulsars

TL;DR

This paper introduces a novel method to measure black hole spin with high precision by analyzing gravitational lensing effects on pulsar signals, focusing on angular shifts and time delays caused by rotation.

Contribution

It derives equations for lensing by rotating black holes and demonstrates how spin affects observable lensing parameters, enabling more accurate spin measurements.

Findings

Frame dragging increases deflection angles for co-rotating light rays.

Rotating black holes cause measurable shifts in image positions and time delays.

Differential time delays can be used to determine black hole spin with less than 1% error.

Abstract

We propose a new procedure for measuring the spin of a black hole with an unprecedented accuracy based on the gravitational lensing of millisecond pulsars. We derive the basic equations for lensing by a rotating black hole. We show that the frame dragging effect increases the deflection angle of a light ray co-rotating with the black hole. For the primary (secondary) images the angular positions are larger (smaller) for a rotating black hole by an amount on the order of tens of microarcseconds. The differential time delay of images for the case in which the lens is a rotating black hole is smaller than that in the case of non-rotating lens of the same mass, and it can be larger than a few milliseconds. We show that this quantity offers the possibility of reducing the error of spin measurement to less than one percent if we could measure the differential time delay with accuracy of microseconds. We also study relativistic images that are produced by light rays that rotate around the black hole before reaching the observer. The angular positions of relativistic images on the same side as the primary (secondary) image are a few microarcseconds larger (smaller) if the black hole is rotating. Furthermore, the differential time delay between relativistic images is about twelve orders of magnitude larger in the case of rotating lens.