248 research outputs found
Curvature invariants in algebraically special spacetimes
It is well known that all curvature invariants of the order zero vanish for
type-III and type-N vacuum spacetimes. We briefly summarize properties of
higher order curvature invariants for these spacetimes.Comment: 2 pages, contribution to the 9th Marcel Grossmann meeting (MG9),
Rome, July 200
Co-accelerated particles in the C-metric
With appropriately chosen parameters, the C-metric represents two uniformly
accelerated black holes moving in the opposite directions on the axis of the
axial symmetry (the z-axis). The acceleration is caused by nodal singularities
located on the z-axis.
In the~present paper, geodesics in the~C-metric are examined. In general
there exist three types of timelike or null geodesics in the C-metric:
geodesics describing particles 1) falling under the black hole horizon;
2)crossing the acceleration horizon; and 3) orbiting around the z-axis and
co-accelerating with the black holes.
Using an effective potential, it can be shown that there exist stable
timelike geodesics of the third type if the product of the parameters of the
C-metric, mA, is smaller than a certain critical value. Null geodesics of the
third type are always unstable. Special timelike and null geodesics of the
third type are also found in an analytical form.Comment: 10 pages, 12 EPS figures, changes mainly in abstract & introductio
Accelerating Kerr-Newman black holes in (anti-)de Sitter space-time
A class of exact solutions of the Einstein-Maxwell equations is presented
which describes an accelerating and rotating charged black hole in an
asymptotically de Sitter or anti-de Sitter universe. The metric is presented in
a new and convenient form in which the meaning of the parameters is clearly
identified, and from which the physical properties of the solution can readily
be interpreted.Comment: 5 pages. To appear in Phys. Rev.
Boost-rotation symmetric vacuum spacetimes with spinning sources
Boost-rotation symmetric vacuum spacetimes with spinning sources which
correspond to gravitational field of uniformly accelerated spinning "particles"
are studied. Regularity conditions and asymptotic properties are analyzed. News
functions are derived by transforming the general spinning boost-rotation
symmetric vacuum metric to Bondi-Sachs coordinates.Comment: REVTeX 4, 9 page
On the algebraic classification of spacetimes
We briefly overview the Petrov classification in four dimensions and its
generalization to higher dimensions.Comment: Submitted to Journal of Physics, conference series, proceedings of
4th meeting on constrained dynamics and quantum gravity, 12-16 September
2005, Sardinia, Ital
Ricci identities in higher dimensions
We explore connections between geometrical properties of null congruences and
the algebraic structure of the Weyl tensor in n>4 spacetime dimensions. First,
we present the full set of Ricci identities on a suitable "null" frame, thus
completing the extension of the Newman-Penrose formalism to higher dimensions.
Then we specialize to geodetic null congruences and study specific consequences
of the Sachs equations. These imply, for example, that Kundt spacetimes are of
type II or more special (like for n=4) and that for odd n a twisting geodetic
WAND must also be shearing (in contrast to the case n=4).Comment: 8 pages. v2: typo corrected between Propositions 2 and 3. v3: typo in
the last term in the first line of (11f) corrected, missing term on the
r.h.s. of (11p) added, first sentence between Propositions 2 and 3 slightly
change
Global aspects of accelerating and rotating black hole space-times
The complete family of exact solutions representing accelerating and rotating
black holes with possible electromagnetic charges and a NUT parameter is known
in terms of a modified Plebanski-Demianski metric. This demonstrates the
singularity and horizon structure of the sources but not that the complete
space-time describes two causally separated black holes. To demonstrate this
property, the metric is first cast in the Weyl-Lewis-Papapetrou form. After
extending this up to the acceleration horizon, it is then transformed to the
boost-rotation-symmetric form in which the global properties of the solution
are manifest. The physical interpretation of these solutions is thus clarified.Comment: 15 pages, 1 figure. To appear in Class. Quantum Gra
Bianchi identities in higher dimensions
A higher dimensional frame formalism is developed in order to study
implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes
of the algebraic types III and N in arbitrary dimension . It follows that
the principal null congruence is geodesic and expands isotropically in two
dimensions and does not expand in spacelike dimensions or does not expand
at all. It is shown that the existence of such principal geodesic null
congruence in vacuum (together with an additional condition on twist) implies
an algebraically special spacetime. We also use the Myers-Perry metric as an
explicit example of a vacuum type D spacetime to show that principal geodesic
null congruences in vacuum type D spacetimes do not share this property.Comment: 25 pages, v3: Corrections to Appendix B as given in
Erratum-ibid.24:1691,2007 are now incorporated (A factor of 2 was missing in
certain Bianchi equations.
Note on Invariants of the Weyl Tensor
Algebraically special gravitational fields are described using algebraic and
differential invariants of the Weyl tensor. A type III invariant is also given
and calculated for Robinson-Trautman spaces.Comment: 3 pages, no figures, corrected expression (12
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