Abstract
We discuss the comments made by Emanuel Gallo and Thomas M\adler on our papers [Gen. Relativ. Gravit. 49, 77 (2017) and Phys. Rev. D 99, 084054 (2019)] on boosted Kerr black holes in general relativity. We considered their criticisms carefully, as they added a significant contribution to the question of boosted Kerr black holes in general relativity examined in our papers. Here, we expand on further results of our papers that were not duly included in the published papers, as noticed by Gallo and M\adler. We now consider the complete asymptotic Lorentz transformations of Robinson-Trautman (RT) coordinates to Bondi-Sachs (BS) asymptotic coordinates of a radiative RT spacetime, which include the perturbation term of the boosted RT metric corresponding to the Lense-Thirring rotation originating from the Kerr metric. The transformation of the rotation parameter $\ensuremath{\omega}$ as the RT coordinates transform to BS coordinates is obtained, as well as the form of the boosted Kerr metric where we make use of the complete asymptotic Lorentz transformation.
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