A Simple Continuous Parametrization of the Kasner Indices

TL;DR

This paper introduces a continuous parametrization of Kasner indices using trilinear coordinates, allowing for a clear visualization of their variation and a time-dependent expression of the parameter.

Contribution

It presents a novel continuous parametrization of Kasner indices based on trilinear coordinates, enhancing understanding of their variation over time.

Findings

Provides a continuous parameterization of Kasner indices

Enables visualization of index variations

Expresses the parameter as a function of time

Abstract

A parametrization of the Kasner indices in terms of a continuous parameter is constructed by exploiting their representation as trilinear coordinates. This provides a clear picture of their variation through their entire range vis a vis each other. The parameter can be expressed as a function of time.