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We discuss junction conditions across null hypersurfaces in a class ofscalar-tensor gravity theories with i) second order dynamics, ii) obeying therecent constraints imposed by gravitational wave propagation, and iii) allowingfor a cosmologically viable evolution. These requirements select kineticgravity braiding models with linear kinetic term dependence and scalarfield-dependent coupling to curvature. We explore a pseudo-orthonormal tetradand its allowed gauge fixing, with one null vector standing as the normal, theother being transversal to the hypersurface. We derive a generalization of theLanczos equation in a 2+1 decomposed form, relating the energy density, currentand isotropic pressure of a distributional source to the jumps in thetransverse curvature and transverse derivative of the scalar. Additionally wediscuss a scalar junction condition and its implications for the distributionalsource.

Lanczos equation on light-like hypersurfaces in a cosmologically viable class of kinetic gravity braiding theories