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

TL;DR

This work shows that Local Sum Rules (LSR) on Randall–Sundrum braneworlds tightly constrain localized matter sources, enabling consistent embeddings of four-dimensional compact objects. It first reaffirms the Chamblin black string as a baseline higher-dimensional solution and then embeds the Ellis–Bronnikov wormhole via a localized phantom scalar, connecting higher-dimensional geometry with known 4D wormhole physics. It then introduces localized nonlinear electrodynamics with a square-root Lagrangian $\mathcal{L}(\mathcal{F}) = -\beta\sqrt{\mathcal{F}}$, deriving magnetic and dyonic braneworld black strings that reduce to Chamblin in the limit $\beta \to 0$ and map onto Letelier and Letelier–Alencar on the brane. Overall, the paper demonstrates how higher-dimensional gravity with localized fields can realize braneworld compact objects that mirror familiar 4D solutions, while highlighting rich magnetic/dyonic parameter spaces and stability avenues for future exploration.

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 $\mathcal{L}(\mathcal{F}) = -β\sqrt{\mathcal{F}}$, 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 $β\to 0$, illustrating how localized higher-dimensional matter fields can consistently support braneworld compact objects and connect higher-dimensional physics with well-known four-dimensional solutions.