Embedding Wormholes and Dyonic Black Strings in Warped Braneworlds via Local Sum Rules

TL;DR

This paper constructs and analyzes localized higher-dimensional objects like wormholes and black strings in warped braneworlds using local sum rules, introducing new solutions supported by nonlinear electrodynamics.

Contribution

It introduces new black string solutions supported by nonlinear electrodynamics and demonstrates their connection to known four-dimensional solutions within the braneworld framework.

Findings

Embedded Ellis-Bronnikov wormhole with scalar field

Derived black string solutions with nonlinear electrodynamics

Solutions reduce to known black strings as parameters vary

Abstract

Building on our previous work [1], where the Local Sum Rules (LSR) were established, we investigate the construction of compact objects in Randall-Sundrum braneworlds supported by matter fields that are dynamically consistent and localizable. We begin by revisiting the Chamblin et al. black string, highlighting its role as a foundational higher-dimensional solution. We then show that the Ellis-Bronnikov wormhole can be consistently embedded in this framework via a localized free scalar field, providing a simple yet nontrivial example of a braneworld compact object. Finally, we derive two novel black string solutions sourced by a localized nonlinear electrodynamics (NED) theory with Lagrangian $\mathcal{L}(\mathcal{F}) = -\beta \sqrt{\mathcal{F}}$, corresponding to purely magnetic and dyonic configurations. The purely magnetic solution reproduces the classical Letelier string cloud on the brane, while the dyonic solution generalizes it to include electric charge, closely paralleling the Letelier-Alencar construction. Both NED solutions reduce smoothly to the Chamblin et al. black string in the limit $\beta \to 0$, illustrating how localized higher-dimensional matter fields can consistently support braneworld compact objects and connect higher-dimensional physics with well-known four-dimensional solutions.