Solution of Stationary and Axisymmetric Problem in General Relativity.Nontraditional Approach

TL;DR

This paper introduces a novel nontraditional method for solving stationary axisymmetric problems in general relativity, leading to new solutions including a 4-parameter vacuum solution and connections to Kerr and NUT solutions.

Contribution

The paper presents a new approach based on essential coordinates aligned with the metric tensor, resulting in a new 4-parameter vacuum solution and links to known solutions like Kerr and NUT.

Findings

Derived a new 4-parameter vacuum solution.

In static case, recovers known GR solutions.

In stationary case, relates to Kerr and NUT solutions.

Abstract

Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach allows to obtain new 4-parametric vacuum solution. In special static case this solution becomes the set well-known GR exact solutions for degenerate vacuum gravitational fields, in some special stationary case, after transformations coincides with Kerr solution. In other special stationary case the founded solution turn into modified NUT solution.