Multidimensional generalization of Kasner solution

TL;DR

This paper extends the Kasner solution to higher dimensions with multiple variables, characterizing solutions via constant matrices and geometric conditions, and analyzing their properties.

Contribution

It provides a full generalization of the Kasner metric for n+1 dimensions with m variables, using matrix parameters and geometric constraints.

Findings

Solutions are characterized by constant matrices of Kasner parameters.

Parameters form Casner hyperspheres in Euclidean space.

The paper analyzes the general properties of these higher-dimensional solutions.

Abstract

Full generalization of Kasner metric for the case of $n+1$ dimensions and $m\le n+1$ essential variables is obtained. Any solution is defined by the corresponding constant matrix of Kasner parameters. This parameters form in euclidian space Casner hyperspheres and are connected by additional conditions. General properties of obtained solutions are analyzed.