Physical Interpretation of Cylindrically Symmetric Static Gravitational Fields

TL;DR

This paper explores the relationship between interior matter properties and exterior spacetime metrics for static cylindrical and spherical distributions in Einstein and Brans-Dicke gravity, establishing conditions for consistency and hydrostatic equilibrium.

Contribution

It derives explicit relations between interior matter characteristics and exterior metrics for cylindrical and spherical bodies in higher-dimensional gravity theories, linking them to hydrostatic equilibrium conditions.

Findings

Derived conditions linking interior matter and exterior metrics.

Established equivalence to hydrostatic equilibrium equations.

Ensured consistent Newtonian limit for the models.

Abstract

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.