On Conformally Flat Stationary Axisymmetric Spacetimes

Details On Conformally Flat Stationary Axisymmetric Spacetimes On Conformally Flat Stationary Axisymmetric Spacetimes

2002-05-17

arxiv.org/abs/gr-qc/0205080v1

Phys.Rev. D66 (2002) 124018; Erratum-ibid. D68 (2003) 049901

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTex4, 5 pages

Scientific paper

10.1103/PhysRevD.68.049901

It is shown that within conformally flat stationary axisymmetric spacetimes, besides of the static family, there exists a new class of metrics, which is always stationary and axisymmetric. All these spacetimes, the static and the stationary ones, are endowed with an arbitrary function depending on the two non--Killingian coordinates. The explicit form of this function can be determined once the coupled matter, i.e., the energy--momentum tensor is given. One might hope possible extensions of this result to black holes on two--branes in four dimensions.

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