Strong gravitational lensing by DHOST black holes

Abstract

The gravitational 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 symmetric spacetimes. We apply this to a set of numerical black hole solutions within the class of modified gravity theories known as degenerate higher order scalar–tensor theories (DHOST). 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 of modified gravity.

Horndeski fermion–boson stars

“…The action (1) represents a large family of scalar-tensor theories, in particular we are interested in those who introduce infrared modifications of gravity. A simple choice of functions L i that represents a low energy effective model was presented in [60] (see also [74][75][76])…”

Distortions of images of Schwarzschild lensing

“…Using tangential and radial magnifications of images, we now use Eq. (19) to compute logarithmic distortions of all these images. We then plot logarithmic distortions δ of 6 images (primary, secondary, and relativistic image of order 1 and 2 on both sides of the optic axis) against β.…”

“…Perlick [13] called this new lens equation an almost exact lens equation. A large number of research papers on strong gravitational field lensing due to black holes [14][15][16][17][18][19][20][21][22][23][24][25][26] and exotic objects such as naked singularities, wormholes, and boson stars [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] have been published (see also references therein. )…”

“…Distances and angular source position play no (extremely insignificant) role in this formula. (See equation (19) in [42].) (ii) The angular separations between any two relativistic images are extremely insensitive to changes in the lens-source distance and angular source position.…”

Horndeski fermion-boson stars

“…The action (1) represents a large family of scalar-tensor theories, in particular we are interested in those who introduce infrared modifications of gravity. A simple choice of functions L i that represents a low energy effective model was presented in [55] (see also [67,68,69])…”