On the uplift of 4D wormholes in Braneworld models and their 5D structure

TL;DR

This paper develops a general method to analyze how 4D wormholes can be embedded in 5D braneworld models, revealing new conditions and features of the bulk structure and the impact of extra dimensions.

Contribution

It introduces an extended General Embedding Algorithm for non-invertible radial functions and derives the first flare-out conditions for braneworld wormholes, highlighting differences from flat extra dimension cases.

Findings

Bulk structure of braneworld wormholes differs from 4D cases.

Warped extra dimensions influence 5D wormhole features.

Extended GEA applies to non-invertible radial functions.

Abstract

Recent developments for the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models in the form of the General Embedding Algorithm (GEA) [Phys.Rev.D 109 (2024) 4, L041501], initiated the program of studying the bulk structure of braneworld wormholes. In this article, adopting a completely generic approach, we derive the general conditions that the metric functions of any braneworld spacetime must satisfy to describe a wormhole structure in the bulk. Particular emphasis is placed on clarifying the proper uplift of 4D spacetimes, expressed in terms of arbitrary radial coordinates on the brane, and we demonstrate the important role of the circumferential radius metric function $r(u)$ for the embedding. To ensure applicability even when $r(u)$ is non-invertible, we develop an extended formulation of the GEA. Additionally, the flare-out conditions for braneworld wormholes are presented for the first time and are found to differ from the case of flat extra dimensions. To illustrate the method, we first perform the uplift into both thin (Randall-Sundrum II) and thick braneworld models for four well-known 4D wormhole spacetimes: the effective braneworld wormhole solutions of Casadio-Fabbri-Mazzacurati and Bronnikov-Kim, the Simpson-Visser spacetime, and the Ellis-Bronnikov or "anti-Fisher" solution. Subsequently, we study their bulk features by means of curvature invariants, flare-out conditions, energy conditions and embedding diagrams. Our analysis reveals that the assumption of a warped extra dimension has non-trivial implications for the structure of 5D wormholes.