Absence of gyratons in the Robinson-Trautman class
arXiv:1406.0729 · doi:10.1103/PhysRevD.89.124029
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.
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
References in corpus (6)
- Robinson-Trautman spacetimes in higher dimensions
- Algebraic classification of higher dimensional spacetimes based on null alignment
- General Kundt spacetimes in higher dimensions
- Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
- Higher-dimensional Kundt waves and gyratons
- Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
Cited by in corpus (5)
- Algebraic classification of Robinson-Trautman spacetimes
- Algebraic structure of Robinson-Trautman and Kundt geometries in arbitrary dimension
- Gyratons in the Robinson-Trautman and Kundt classes
- Solutions with pure radiation and gyratons in 3D massive gravity theories
- Higher dimensional Robinson-Trautman spacetimes sourced by p-forms: static and radiating black holes