Strong lensing by DHOST black holes

TL;DR

This paper develops a hybrid analytic-numerical method to accurately compute light deflection in strong gravitational fields of DHOST black holes, enabling tests of alternative gravity theories through strong lensing observations.

Contribution

It introduces a new hybrid approximation technique for calculating deflection angles in DHOST black holes, facilitating efficient analysis of strong lensing effects.

Findings

The method accurately matches full numerical results for various photon trajectories.

Strong lensing effects in DHOST black holes can be comparable to observational uncertainties.

Strong lensing can serve as a tool to constrain DHOST theories with current data.

Abstract

The deflection of light in the strong field limit is an important test for alternative theories of gravity. However, solutions for the metric that allow for analytic computations are not always available. We implement a hybrid analytic-numerical approximation to determine the deflection angle in static, spherically symmetrics pacetimes. We apply this to a set of numerical black hole solutions within the class of theories known as Degenerate Higher Order Scalar-tensor Theories. Comparing our results to a more time consuming full numerical integration, we find that we can accurately describe the deflection angle for light rays passing at arbitrary distances from the photon sphere with a combination of two analytic-numerical approximations. Furthermore, we find a range of parameters where our DHOST black holes predict strong lensing effects whose size is comparable with the uncertainty in the properties of the supermassive black hole in M87 reported by the Event Horizon Telescope, showing that strong lensing is a viable alternative to put constraints on these models.