Classification of Einstein equations with cosmological constant in warped product space-time

TL;DR

This paper classifies various warped product space-times and derives the Einstein equations with cosmological constant to uniquely determine warp functions, advancing understanding of their geometric and physical properties.

Contribution

It introduces a comprehensive classification of warped product space-times and derives Einstein equations specific to each class, providing a systematic approach to determine warp functions.

Findings

Classification into three categories of warped space-times.

Derivation of Einstein equations with cosmological constant for each class.

Unique determination of warp functions based on Einstein equations.

Abstract

We classify all warped product space-times in three categories as i) generalized twisted product structures, ii) base conformal warped product structures and iii) generalized static space-times and then we obtain the Einstein equations with the corresponding cosmological constant by which we can determine uniquely the warp functions in these warped product space-times.