Sequential Warped Products: Curvature and Killing Vector Fields

TL;DR

This paper introduces sequential warped products, a new geometric construction that broadens the scope of solutions to Einstein's equations, and analyzes their curvature, geodesics, and vector fields.

Contribution

It defines and studies the geometry of sequential warped products, deriving curvature formulas and characterizations of geodesics and conformal vector fields.

Findings

Derived covariant derivatives, curvature tensor, Ricci curvature, and scalar curvature formulas.

Characterized geodesics and conformal vector fields on these manifolds.

Analyzed specific models like sequential generalized Robertson-Walker spacetimes.

Abstract

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker spacetimes and sequential standard static spacetimes.