Photon rockets moving arbitrarily in any dimension

A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes photon rockets accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so that the acceleration of the rocket need not be uniform - both its magnitude and direction may vary with time. Except at location of the point-like rocket the spacetimes have no curvature singularities, and topological defects like cosmic strings are also absent. Any value of a cosmological constant is allowed. We investigate some particular examples of motion, namely a straight flight and a circular trajectory, and we derive the corresponding radiation patterns and the mass loss of the rockets. We also demonstrate the absence of "gravitational aberration" in such spacetimes. This interesting member of the higher-dimensional Robinson-Trautman class of pure radiation spacetimes of algebraic type D generalises the class of Kinnersley's solutions that has long been known in four-dimensional general relativity.Comment: Text and figures modified (22 pages, 8 figures). To appear in the International Journal of Modern Physics D, Vol. 20, No..

Gravitational and electromagnetic fields near an anti-de Sitter-like infinity

We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.Comment: 4 pages, 2 figure

Geodesics in spacetimes with expanding impulsive gravitational waves

We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For the special class of axially symmetric spacetimes with the spherical impulse generated by a snapping cosmic string we give a detailed physical interpretation of the motion of test particles.Comment: 12 pages, Revtex, final versio

Ultrarelativistic boost of the black ring

We investigate the ultrarelativistic boost of the five-dimensional Emparan-Reall non-rotating black ring. Following the classical method of Aichelburg and Sexl, we determine the gravitational field generated by a black ring moving ``with the speed of light'' in an arbitrary direction. In particular, we study in detail two different boosts along axes orthogonal and parallel to the plane of the ring circle, respectively. In both cases, after the limit one obtains a five-dimensional impulsive pp-wave propagating in Minkowski spacetime. The curvature singularity of the original static spacetime becomes a singular source within the wave front, in the shape of a ring or a rod according to the direction of the boost. In the case of an orthogonal boost, the wave front contains also a remnant of the original disk-shaped membrane as a component of the Ricci tensor (which is everywhere else vanishing). We also analyze the asymptotic properties of the boosted black ring at large spatial distances from the singularity, and its behaviour near the sources. In the limit when the singularity shrinks to a point, one recovers the well known five-dimensional analogue of the Aichelburg-Sexl ``monopole'' solution.Comment: 10 pages, 2 figures, REVTeX 4. v2: added boost in an arbitrary direction, one new figure, one new reference. To appear in Phys. Rev.

Cylindrically and toroidally symmetric solutions with a cosmological constant

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and Tian. In particular, when the cosmological constant is positive, the spacetimes have toroidal symmetry. One of the two curvature singularities can be removed by matching the Linet-Tian vacuum solution across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. Some other properties and limiting cases of these space-times are also described, together with their generalisation to higher dimensions.Comment: 4 pages, 2 figures. To appear in the Proceedings of The Spanish Relativity Meeting (ERE2010), Journal of Physics: Conference Serie

Asymptotic structure of radiation in higher dimensions

We characterize a general gravitational field near conformal infinity (null, spacelike, or timelike) in spacetimes of any dimension. This is based on an explicit evaluation of the dependence of the radiative component of the Weyl tensor on the null direction from which infinity is approached. The behaviour similar to peeling property is recovered, and it is shown that the directional structure of radiation has a universal character that is determined by the algebraic type of the spacetime. This is a natural generalization of analogous results obtained previously in the four-dimensional case.Comment: 14 pages, no figures (two references added

Higher-dimensional Kundt waves and gyratons

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

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson's high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti--)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.Comment: 14 pages, 8 figures, to appear in Czech. J. Phy

Robinson-Trautman spacetimes in higher dimensions

As an extension of the Robinson-Trautman solutions of D=4 general relativity, we investigate higher dimensional spacetimes which admit a hypersurface orthogonal, non-shearing and expanding geodesic null congruence. Einstein's field equations with an arbitrary cosmological constant and possibly an aligned pure radiation are fully integrated, so that the complete family is presented in closed explicit form. As a distinctive feature of higher dimensions, the transverse spatial part of the general line element must be a Riemannian Einstein space, but it is otherwise arbitrary. On the other hand, the remaining part of the metric is - perhaps surprisingly - not so rich as in the standard D=4 case, and the corresponding Weyl tensor is necessarily of algebraic type D. While the general family contains (generalized) static Schwarzschild-Kottler-Tangherlini black holes and extensions of the Vaidya metric, there is no analogue of important solutions such as the C-metric.Comment: 11 page

General Kundt spacetimes in higher dimensions

We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subclasses of the Kundt family and we identify the most important special cases, namely generalised pp-waves, VSI or CSI spacetimes, and gyratons.Comment: 15 page