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arXiv · 1406.0729

Absence of gyratons in the Robinson-Trautman class

Robert Svarc·Jiri Podolsky
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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.

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Robert Svarc, Jiri Podolsky. 2019-03-04. Absence of gyratons in the Robinson-Trautman class. https://doi.org/10.1103/physrevd.89.124029

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