# Light bending and gravitational lensing in Brans-Dicke theory

## TL;DR

This paper develops a formalism to calculate higher-order light bending and gravitational lensing effects in Brans-Dicke theory and compares these predictions to general relativity, revealing parameter-dependent corrections.

## Contribution

It introduces a general method for higher-order lensing corrections in scalar-tensor theories and applies it specifically to Brans-Dicke theory, highlighting new correction terms.

## Key findings

- Higher-order corrections depend on the gravity theory.
- Total magnification has a non-zero first-order correction.
- Lensing observables approach GR results as ω tends to +∞.

## Abstract

As an important candidate theory of gravity, Brans-Dicke theory has been widely studied. In this paper, we investigate light bending and gravitational lensing by compact objects in Brans-Dicke theory in weak gravitational field. Firstly, we present a general formalism for calculating higher-order corrections to light bending angle and lensing observables for a static, spherically symmetric and flat spacetime, in which the metric is given in the isotropic coordinates. Secondly, we apply the general formalism to Brans-Dicke theory and get the corresponding light bending angle and lensing observables. Our results show that, although the sums over the low-order correction terms in magnifications of the primary and secondary images do not dependent on the theories of gravity, the sums over correction terms with order higher than three do. Moreover, we show that the total magnification has a non-vanishing first-order correction, rather than a vanishing contribution concluded in the literature. We find that the corrections to lensing observables of BD theory close to those of GR when the parameter $\omega$ tends to $+\infty$ from $-\frac32$, while opposition occurs when $\omega$ tends to $-2$ from $-\infty$.