Review Reports

Round 1

Reviewer 1 Report

There are several points respect to this paper. The work is based in ref(24) by the authors, however, it is important to mention some points before it could be consider for publication.

The paper is mainly about gravitational lensing in the "weak field approximation" of a solution called "Boosted Kerr black hole" ref(23). With respect to this solution there is an important paper "Comment on Boosted Kerr black holes in GR" arxiv:1906.08761 where some important issues about using gravitational lensing to study this solution face some difficulties. It is important in the present work address properly the discussion about.

The section 2 of the present paper is almost identical to the section 2 of the reference "Gravitational lensing in a non-uniform plasma" G.S. Bisnovatyi et al. MNRAS 404, 1790-1800 (2010). It is important to emphasize that the MNRASreference is very clear in the problem to solve: The Schwarzschild lens with a sorrounding plasma in the weak limit (very well established, and from this approach they study the plasma effect with some density profiles as SIS, ..etc. It is important to mention that references as Schneider et al. are very clear in what weak limit means and how is the ray tracing for the lens equation), in the present work some physical aspects as the discussionabout the weak field limit, the lens equation,...are missing and it is difficult to evaluate the contribution.  

It could be very interesting for this contribution to compare the results with references as "gravitational lens with angular momentum" A&A 114, 175-180. J. Ibanez 1983 or with the reference (13). 

In the end, taking into account that most of the results come from ref(24), a major revision it is neccesary before consider the present work for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf