Characteristics of conformal Ricci soliton on warped product spaces

TL;DR

This paper investigates conformal Ricci solitons on warped product manifolds, establishing their properties, characterizations, and implications for specific spacetime models like generalized Robertson-Walker spacetimes.

Contribution

It extends the study of conformal Ricci solitons to warped product manifolds, providing new characterizations and conditions, including their behavior on base and fiber components.

Findings

Warped product manifolds with conformal Ricci solitons have base and fiber sharing the property.

Conformal Ricci solitons characterized by Killing and conformal vector fields on warped products.

Warped product manifolds with conformal Ricci solitons and concurrent potential vector fields are Ricci flat.

Abstract

Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual Riemannian product manifolds. First, we prove that if a warped product manifold admits conformal Ricci soliton then the base and the fiber also share the same property. In the next section the characterization of conformal Ricci solitons on warped product manifolds in terms of Killing and conformal vector fields has been studied. Next, we prove that a warped product manifold admitting conformal Ricci soliton with concurrent potential vector field is Ricci flat. Finally, an application of conformal Ricci soliton on a class of warped product spacetimes namely, generalized Robertson-Walker spacetimes has been discussed.