An Elementary Derivation of the Five Dimensional Myers-Perry Metric

TL;DR

This paper presents a straightforward derivation of the five-dimensional Myers-Perry black hole metric by solving Einstein's equations directly using a simplified Ricci tensor approach.

Contribution

It introduces an elementary method for deriving higher-dimensional black hole metrics, simplifying previous complex calculations.

Findings

Derivation of the 5D Myers-Perry metric using a simple Ricci tensor approach.

The method avoids second derivatives, making the derivation more accessible.

Provides a new pedagogical approach to higher-dimensional Einstein solutions.

Abstract

We derive the five dimensional Myers-Perry metric via an elementary method to solve the vacuum Einstein field equations directly. This method firstly proposed by Clotz is very simple since it merely involves four components of Ricci tensor and only requires us to deal with some equations without second derivatives' terms when the metric ansatz is assumed to take an appropriate form.