Absence of gyratons in the Robinson-Trautman class

作者：Svarc R^*; Podolsky J

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2014, 89(12): 124029.

DOI：10.1103/PhysRevD.89.124029

We present the Riemann and Ricci tensors for a fully general nontwisting and shear-free geometry in arbitrary dimension D. This includes both the nonexpanding 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., a 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.

• 出版日期2014-6-25