Einstein Product Metrics in Diverse Dimensions

TL;DR

This paper introduces a method for constructing new Einstein Metrics solutions in various dimensions by using direct products, exemplified with three families involving Kerr and (anti-)de Sitter geometries.

Contribution

It presents a novel technique for generating Einstein Metrics solutions through direct product constructions, expanding the set of known solutions in higher dimensions.

Findings

Constructed new Einstein Metrics solutions with cosmological constant.

Demonstrated the method with three families involving Kerr and (anti-)de Sitter geometries.

Provided explicit examples of higher-dimensional Einstein solutions.

Abstract

We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter, Kerr/anti-de Sitter X anti-de Sitter and Kerr X Kerr.