Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

TL;DR

This paper proposes a method to estimate the distance to black holes using the time delay between relativistic images caused by gravitational lensing, which can be measured for supermassive black holes.

Contribution

It introduces a novel approach linking time delay measurements to black hole distance and mass estimation in strong gravitational fields.

Findings

Time delay between images is proportional to the impact angle.

Ratio of time delay to impact angle provides a precise distance measure.

Time delays are measurable for supermassive black holes within the Local Group.

Abstract

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10^8 - 10^9 solar masses in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.