Abstract
Most of the paper treats axisymmetric vacuum solutions of Einstein’s equations that are time-dependent and also invariant under azimuthal inversion. The canonical line element of the analytic solutions is shown to entail only three functions. Their axial expansions converge in a neighbourhood of the axis and provide the general solution, being constructed from an arbitrary function
g
00
|
ρ = 0
=
F
(
t, z
). (Its special cases
F
(
t
) and
F
(
z
) generate, respectively, the cylindrical wave solutions of Einstein-Rosen and the static solutions of Weyl.) In the last section, the canonical line element is extended to include rotational solutions, such as the Kerr stationary one. Its event horizon appears as a disc.
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3. On gravitational waves
4. Forsyth A. R. 1906 Theory of differential equations vol. 5. Cambridge University Press.
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