General Solutions to Static Plane Symmetric Einstein's Equations

TL;DR

This paper derives a general explicit formula for static plane symmetric Einstein's equations with a cosmological constant, encompassing various specific solutions like vacuum, perfect fluid, and charged plane cases.

Contribution

It provides a unified, explicit solution framework for static plane symmetric Einstein's equations with a cosmological constant, including new solutions with linear relations among energy-momentum components.

Findings

Derived explicit general solution formula.

Obtained specific solutions for vacuum, perfect fluid, and charged plane.

Compared new solutions with known results.

Abstract

A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the vacuum with cosmological constant, the perfect fluid with a linear equation of state and the electrically charged plane are derived and compared with known results. The general solution with a linear relation among the energy-momentum tensor components is also obtained.