39 research outputs found
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