Strong Gravitational Lensing in Horndeski theory

In this paper we build the general formalism of gravitational lensing in luminal Horndeski theories, deriving the Jacobi matrix equation and the general angular diameter distance in these theories through the screen space formalism. We generalize the focusing and multiple lensing theorems to include Scalar Tensor theories belonging to the class and derive constraints they must satisfy to exhibit the same gravitional lensing behavior predicted by General Relativity. This provides a way to test theories through Strong Lensing effects, as well as a full theoretical framework for testing lensing in these theories. We find that for some subclasses, like metric $f(R)$ and unified $k$-essence, the conditions are satisified in general physical cases, while for others like Galileon Condensate models, the conditions impose constraints on the parameter space of the theory.