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Register a new userConformally flat sources for the Linet-Tian spacetime
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We investigate the matching, across cylindrical surfaces, of static cylindrically symmetric conformally flat spacetimes with a cosmological constant $Lambda$, satisfying regularity conditions at the axis, to an exterior Linet-Tian spacetime. We prove that for $Lambdaleq 0$ such matching is impossible. On the other hand, we show through simple examples that the matching is possible for $Lambda>0$. We suggest a physical argument that might explain these results.
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We investigate the geodesics kinematics and dynamics in the Linet-Tian metric with Lambda<0 and compare with the results for the Levi-Civita metric, when Lambda=0. This is used to derive new stability results about the geodesics dynamics in static vacuum cylindrically symmetric spacetimes with respect to the introduction of Lambda<0. In particular, we find that increasing |Lambda| always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any Lambda<0 breaks the geodesics orbit confinement of the Lambda=0 metric, for both planar and non-planar null geodesics, which are therefore unstable. Using the full system of geodesics equations, we provide numerical examples which illustrate our results.
We analyse the geodesics dynamics in cylindrically symmetric vacuum spacetimes with Lambda>0 and compare it to the Lambda=0 and Lambda<0 cases. When Lambda>0 there are two singularities in the metric which brings new qualitative features to the dynamics. We find that Lambda=0 planar timelike confined geodesics are unstable against the introduction of a sufficiently large Lambda, in the sense that the bounded orbits become unbounded. In turn, any non-planar radially bounded geodesics are stable for any positive Lambda. We construct global non-singular static vacuum spacetimes in cylindrical symmetry with Lambda>0 by matching the Linet-Tian metric with two appropriate sources.
The static, apparently cylindrically symmetric vacuum solution of Linet and Tian for the case of a positive cosmological constant $Lambda$ is shown to have toroidal symmetry and, besides $Lambda$, to include three arbitrary parameters. It possesses two curvature singularities, of which one can be removed by matching it across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. In four dimensions, this clarifies the geometrical properties, the coordinate ranges and the meaning of the parameters in this solution. Some other properties and limiting cases of this space-time are described. Its generalisation to any higher number of dimensions is also explicitly given.
The complete class of conformally flat, pure radiation metrics is given, generalising the metric recently given by Wils.
We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form, with the extrinsic curvature of a Kerr slice. We study these new initial data representing spinning black holes by numerically solving the Hamiltonian constraint. They have the following features: i) Contain less radiation, for all allowed values of the rotation parameter, than the corresponding single spinning Bowen-York black hole. ii) The maximum rotation parameter $J/m^2$ reached by this solution is higher than that of the purely longitudinal solution allowing thus to describe holes closer to a maximally rotating Kerr one. We discuss the physical interpretation of these properties and their relation with the weak cosmic censorship conjecture. Finally, we generalize the data for multiple black holes using the ``puncture and isometric formulations.
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