The time delay in strong gravitational lensing with Gauss-Bonnet correction

TL;DR

This paper investigates how Gauss-Bonnet gravity influences the time delay in strong gravitational lensing, deriving expressions and analyzing the effects of the coupling parameter on observable delays.

Contribution

It provides a new analytical expression for the time delay in lensing under Gauss-Bonnet gravity and explores the impact of the coupling parameter on the delay behavior.

Findings

Time delay increases with larger separation between images.

Time delay diverges as the Gauss-Bonnet parameter approaches a critical value.

The ratio of Gauss-Bonnet coefficient to mass affects the delay significantly.

Abstract

The time delay between two relativistic images in the strong gravitational lensing governed by Gauss-Bonnet gravity is studied. We derive and calculate the expression of time delay due to the Gauss-Bonnet coupling. It is shown that the time delay for two images with larger space each other is longer. We also find that the ratio of Gauss-Bonnet coefficient and the mass of gravitational source changes in the region like $\frac{\alpha}{M}\in[0,2)$. The time delay is divergent with $\frac{\alpha}{M}\longrightarrow 2$.