Solution of Einstein Field Equations for Anisotropic Matter with Vanishing Complexity: Spacetime Metric Satisfying Karmarkar Condition and Conformally Flat Geometry

TL;DR

This paper derives a unique solution to Einstein's field equations for a static, spherically symmetric spacetime with anisotropic matter, satisfying the Karmarkar condition and being conformally flat, with zero complexity.

Contribution

It proves that only one spacetime metric satisfies the combined conditions of vanishing complexity, Karmarkar condition, and conformal flatness in this context.

Findings

Only one solution meets all three conditions.

The solution confirms the uniqueness of such spacetimes.

The metric satisfies Einstein's field equations for anisotropic matter.

Abstract

The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar condition and is conformally flat. It has been noted that there is only one solution that meets these three conditions. This has been shown as a proof of the theorem.