PHYSICAL INTERPRETATION OF CYLINDRICALLY SYMMETRICAL STATIC GRAVITATIONAL-FIELDS

An explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the ext erior space-time according to Einstein gravity for space-time dimensio nality larger than or equal to four. This is achieved through use of a coordinate system isotropic in the transverse coordinates. As a corol lary, 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 param eters characterizing the exterior metric. It is shown that these condi tions are equivalent to the requirement of hydrostatic equilibrium of the matter distribution (generalized Oppenheimer-Volkoff equations). T hese conditions lead to a consistent Newtonian limit where pressures a nd the gravitational constant go to zero at the same rate.