Black string corrections in variable tension braneworld scenarios

TL;DR

This paper investigates how variable brane tension influences black string horizons in braneworld models, revealing significant modifications due to higher-order covariant derivatives and providing new physical insights into these scenarios.

Contribution

It introduces third-order expansion terms in the metric, capturing covariant derivatives of brane tension and their effects on black string horizons, extending previous second-order analyses.

Findings

Black string horizon is significantly affected by variable tension terms.

Higher-order derivatives introduce new physical features.

Model based on Eotvos branes shows notable horizon modifications.

Abstract

Braneworld models with variable tension are investigated, and the corrections on the black string horizon along the extra dimension are provided. Such corrections are encrypted in additional terms involving the covariant derivatives of the variable tension on the brane, providing profound consequences concerning the black string horizon variation along the extra dimension, near the brane. The black string horizon behavior is shown to be drastically modified by the terms corrected by the brane variable tension. In particular, a model motivated by the phenomenological interesting case regarding Eotvos branes is investigated. It forthwith provides further physical features regarding variable tension braneworld scenarios, heretofore concealed in all previous analysis in the literature. All precedent analysis considered uniquely the expansion of the metric up to the second order along the extra dimension, what is able to evince solely the brane variable tension absolute value. Notwithstanding, the expansion terms aftermath, further accomplished in this paper from the third order on, elicits the successive covariant derivatives of the brane variable tension, and their respective coupling with the extrinsic curvature, the Weyl tensor, and the Riemann and Ricci tensors, as well as the scalar curvature. Such additional terms are shown to provide sudden modifications in the black string horizon in a variable tension braneworld scenario