Physical Interpretation of Cylindrically Symmetric Static Gravitational Fields

Details Physical Interpretation of Cylindrically Symmetric Static Gravitational Fields Physical Interpretation of Cylindrically Symmetric Static Gravitational Fields

1997-05-15

arxiv.org/abs/gr-qc/9705044v1

Phys.Rev.D56:3371-3380,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, RevTex, no figures

Scientific paper

10.1103/PhysRevD.56.3371

The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to four. This is achieved through use of a coordinate system isotropic in the transverse coordinates. As a corollary, similar results are obtained for a spherical matter distribution in Brans-Dicke gravity for dimensions larger than or equal to three. The approach used here leads to consistency conditions for those parameters characterizing the exterior metric. It is shown that these conditions are equivalent to the requirement of hydrostatic equilibrium of the matter distribution (generalized Oppenheimer-Volkoff equations). These conditions lead to a consistent Newtonian limit where pressures and the gravitational constant go to zero at the same rate.

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