On the local form of static plane symmetric space-times in the presence of matter

TL;DR

This paper derives explicit metric forms for static plane-symmetric spacetimes with matter, expressing solutions directly in terms of energy density and pressures, and recovers many known solutions as special cases.

Contribution

It provides a general method to express the metric explicitly in terms of matter variables for static plane-symmetric spacetimes, including a broad class of solutions.

Findings

Explicit metric forms in terms of energy density and pressures

General solution for linearly related pressures and energy density

Recovery of most known static plane-symmetric solutions

Abstract

For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for self-gravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.