Absence of gyratons in the Robinson-Trautman class
Abstract
We present the Riemann and Ricci tensors for a fully general non-twisting and shear-free geometry in arbitrary dimension D. This includes both the non-expanding Kundt and expanding Robinson-Trautman family of spacetimes. As an interesting application of these explicit expressions we then integrate the Einstein equations and prove a surprising fact that in any D the Robinson-Trautman class does not admit solutions representing gyratonic sources, i.e., matter field in the form of a null fluid (or particles propagating with the speed of light) with an additional internal spin. Contrary to the closely related Kundt class and pp-waves, the corresponding off-diagonal metric components thus do not encode the angular momentum of some gyraton. Instead, we demonstrate that in standard D=4 general relativity they directly determine two independent amplitudes of the Robinson-Trautman exact gravitational waves.
Keywords
Cite
@article{arxiv.1406.0729,
title = {Absence of gyratons in the Robinson-Trautman class},
author = {Robert Svarc and Jiri Podolsky},
journal= {arXiv preprint arXiv:1406.0729},
year = {2019}
}
Comments
ATTENTION: The evaluation of equations (54), (55) is incorrect in this paper. This mistake lead us to the incorrect statement about the nonexistence of gyratons within the Robinson-Trautman class. Since the overall results are completely changed, we have published the detailed correction and Erratum, with explicit general RT gyratons, in Phys. Rev. D 99, 044004 (2019); arXiv:1812.02635