Canonical forms for axial symmetric space-times

Carlson, George T.; Safko, John L.

doi:10.1016/0003-4916(80)90057-3

Cited by 20 publications

(16 citation statements)

References 7 publications

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“…The geometry of axisymmetric spacetimes in the vicinity of the axis was studied in [18] (see also [17,19]). It then follows that g t must tend to zero when !…”

Section: The Super-poynting Vector In a Neighborhood Of The Axismentioning

confidence: 99%

Frame dragging and superenergy

2007

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“…The geometry of axisymmetric spacetimes in the vicinity of the axis was studied in [18] (see also [17,19]). It then follows that g t must tend to zero when !…”

Section: The Super-poynting Vector In a Neighborhood Of The Axismentioning

confidence: 99%

Frame dragging and superenergy

2007

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“…Now, from the regularity conditions, necessary to ensure elementary flatness in the vicinity of the axis of symmetry, and in particular at the center (see [12], [13], [14]), we should require that as r ≈ 0…”

Section: The Perfect Geodesic Fluidmentioning

confidence: 99%

Shearing and geodesic axially symmetric perfect fluids that do not produce gravitational radiation

et al. 2015

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Using a framework based on the 1 + 3 formalism we carry out a study on axially and reflection symmetric perfect and geodesic fluids, looking for possible models of sources radiating gravitational waves. Therefore, the fluid should be necessarily shearing, for otherwise the magnetic part of the Weyl tensor vanishes, leading to a vanishing of the super-Poynting vector. However, for the family of perfect, geodesic fluids considered here, it appears that all possible cases reduce to conformally flat, shear-free, vorticity-free, fluids, i.e Friedmann-Roberston-Walker. The super-Poynting vector vanishes and therefore no gravitational radiation is expected to be produced. The physical meaning of the obtained result is discussed.

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“…Now imposing invariance under the inversion requires gi3 = 0, so we are left with seven metric coefficients (Bondi et at. 1962;Carlson & Safko 1980). By the implicit function theorem, the transformation xQ = xQ , x1 =…”

Section: Time-dependent Axisymmetric Gravitation 51mentioning

confidence: 99%

Canonical solution of the equations of axisymmetric gravitation including time dependence

Waylen

1987

Proc. R. Soc. Lond. A

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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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Canonical forms for axial symmetric space-times

Cited by 20 publications

References 7 publications

Frame dragging and superenergy

Frame dragging and superenergy

Shearing and geodesic axially symmetric perfect fluids that do not produce gravitational radiation

Canonical solution of the equations of axisymmetric gravitation including time dependence

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