20 research outputs found
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
Relativistic Solenoids
We construct a general relativistic analogy of an infinite solenoid, i.e., of
an infinite cylinder with zero electric charge and non-zero electric current in
the direction tangential to the cylinder and perpendicular to its axis. We
further show that the solution has a good weak-field limit.Comment: 9 pages, 2 figure
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
Cylindrical spacetimes with a cosmological constant and their sources
We review and investigate some basic properties of static, cylindrically
symmetric spacetimes with non-zero cosmological constant, find non-singular
sheet sources of these spacetimes and discuss their characteristics, and
clarify their relation to the 4D black-string solutions.Comment: 15 pages, 2 figure
Report on workshop A1: Exact solutions and their interpretation
I report on the communications and posters presented on exact solutions and
their interpretation at the GRG18 Conference, Sydney.Comment: 9 pages, no figures. Many typos corrected. Report submitted to the
Proceedings of GR18. To appear in CQ
Static solutions of Einstein's equations with cylindrical symmetry
In analogy with the standard derivation of the Schwarzschild solution, we
find all static, cylindrically symmetric solutions of the Einstein field
equations for vacuum. These include not only the well known cone solution,
which is locally flat, but others in which the metric coefficients are powers
of the radial coordinate and the space-time is curved. These solutions appear
in the literature, but in different forms, corresponding to different
definitions of the radial coordinate. Because all the vacuum solutions are
singular on the axis, we attempt to match them to "interior" solutions with
nonvanishing energy density and pressure. In addition to the well known "cosmic
string" solution joining on to the cone, we find some numerical solutions that
join on to the other exterior solutions.Comment: 16 pages, 5 figures, 3 tables; many literature citations removed from
main body; added historical section to put project into context and include
additional reference