Generalized multiplane gravitational lensing: time delays, recursive lens equation, and the masssheet transformation
Abstract
We consider several aspects of the generalized multiplane gravitational lens theory, in which light rays from a distant source are affected by several main deflectors, and in addition by the tidal gravitational field of the largescale matter distribution in the Universe when propagating between the main deflectors. Specifically, we derive a simple expression for the timedelay function in this case, making use of the general formalism for treating light propagation in inhomogeneous spacetimes which leads to the characterization of distance matrices between main lens planes. Applying Fermat's principle, an alternative form of the corresponding lens equation is derived, which connects the impact vectors in three consecutive main lens planes, and we show that this form of the lens equation is equivalent to the more standard one. For this, some general relations for cosmological distance matrices are derived. The generalized multiplane lens situation admits a generalized masssheet transformation, which corresponds to uniform isotropic scaling in each lens plane, a corresponding scaling of the deflection angle, and the addition of a tidal matrix (mass sheet plus external shear) to each main lens. The scaling factor in the lens planes exhibits a curious alternating behavior for odd and even numbered planes. We show that the time delay for sources in all lens planes scale with the same factor under this generalized masssheet transformation, thus precluding the use of timedelay ratios to break the masssheet transformation.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 2019
 DOI:
 10.1051/00046361/201424881
 Bibcode:
 2019A&A...624A..54S
 Keywords:

 cosmological parameters;
 gravitational lensing: strong