Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes

TL;DR

This paper develops a perturbative method to analyze the deflection of signals in higher-dimensional and asymptotically non-flat spacetimes, revealing how spacetime parameters influence gravitational lensing in various theoretical models.

Contribution

It introduces a unified perturbative approach for calculating deflection angles in complex spacetimes, including higher dimensions and non-flat geometries, extending previous methods.

Findings

Deflection angles follow a (quasi-)series in impact parameter, accounting for finite source and observer distances.

In n-dimensional spacetimes, deflection scales as (M/b)^{n-3} at leading order.

In asymptotically non-flat spacetimes, the deflection angle at trivial order deviates from π.

Abstract

Using a perturbative technique, in this work we study the deflection of null and timelike signals in the extended Einstein-Maxwell spacetime, the Born-Infeld gravity and the charged Ellis-Bronnikov (CEB) spacetime in the weak field limit. The deflection angles are found to take a (quasi-)series form of the impact parameter, and automatically takes into account the finite distance effect of the source and observer. The method is also applied to find the deflections in CEB spacetime with arbitrary dimension. It's shown that to the leading non-trivial order, the deflection in some $n$-dimensional spacetimes is of the order $\mathcal{O}(M/b)^{n-3}$. We then extended the method to spacetimes that are asymptotically non-flat and studied the deflection in a nonlinear electrodynamical scalar theory. The deflection angle in such asymptotically non-flat spacetimes at the trivial order is found to be not $\pi$ anymore. In all these cases, the perturbative deflection angles are shown to agree with numerical results extremely well. The effects of some nontrivial spacetime parameters as well as the signal velocity on the deflection angles are analyzed.