A Class of Higher-Dimensional Solutions of Einstein's Vacuum Equation

TL;DR

This paper introduces a new class of exact higher-dimensional solutions to Einstein's vacuum equations, generalizing Kasner spacetime and revealing complex algebraic structures when the metric involves non-diagonal matrices.

Contribution

It presents novel higher-dimensional vacuum solutions expressed via exponential of symmetric matrices, including new non-diagonal cases not previously documented.

Findings

Solutions generalize Kasner spacetime with cosmological constant

Non-diagonal metrics exhibit intricate algebraic structures

First presentation of these solutions in the literature

Abstract

A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to higher-dimensional generalizations of Kasner spacetime with a cosmological constant. On the other hand, the metrics attained when such matrix is non-diagonal have more intricate algebraic structures. Such solutions have not been presented in the literature yet.