Higher-dimensional Kundt waves and gyratons

Abstract

We present and analyze exact solutions of the Einstein-Maxwell equations in higher dimensions which form a large subclass of the Kundt family of spacetimes. We assume that the cosmological constant may be nonvanishing, and the matter consists of a background aligned electromagnetic field and an additional pure radiation (gyratonic) field with a spin. We show that the field equations reduce to a set of linear equations on the transverse space which can be solved exactly and expressed in terms of the Green functions. We thus find explicit exact gyratonic gravitational and electromagnetic fields created by a radiation beam of null matter with arbitrary profiles of energy density and angular momenta. In the absence of the gyratonic matter we obtain pure nonexpanding higher-dimensional gravitational waves. In particular, we investigate gyratons and waves propagating on backgrounds which are a direct-product of 2-spaces of constant curvature. Such type D or 0 background spacetimes generalize 4-dimensional Nariai, anti-Nariai and Plebanski-Hacyan universes, and conformally flat Bertotti-Robinson and Minkowski spaces. These spacetimes belong to a wider class of spaces which admit the Kahler structure related to the background magnetic field. The obtained wave and gyraton solutions are also members of the recently discussed class of spacetimes with constant scalar invariants (CSI) of the curvature tensor.Comment: 18 pages, no figure

Gyratons in the Robinson-Trautman and Kundt classes

“…In fact, this f p = 0 subclass of Kundt spacetimes (66)-(71) contains all particular gyratonic solutions discussed in the literature so far, see [22,23] for a review and a list of references.…”

“…Einstein's equations for the metric g ab read R ab − 1 2 R g ab + Λ g ab = 8π T ab , where Λ is any cosmological constant. We study spacetimes with a gyratonic matter aligned with k [16,18,22]. In the coordinates of (1), the nonvanishing components of the energy-momentum tensor T ab are T uu (r, u, x) , T up (r, u, x) ,…”

Kundt spacetimes minimally coupled to scalar field

“…If we plug this expression back into (21,22) and consider the first-order terms in v we immediately conclude that has to vanish unless…”

“…If this additional term creates a new contribution to the energy-momentum tensor components T ux , T uv and generates a certain nonvanishing contour integral in the transversal 2-space it is possible to interpret it as a so-called gyraton [22] (gravitational field created by a source with internal rotation).…”

“…Such an alignment means that scalar field propagates along this null direction and can be interpreted as a scalar wave. From the Einstein tensor components (21), (22) for the metric (47) and the form of the scalar field we obtain M ,x = 0 = M ,y . This leads to a simplified form of H [see (17)]…”