Black string corrections in variable tension braneworld scenarios

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, which 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. Braneworld models perform a distinct branch of high- energy physics. Several of the main ideas concerning such models were inspired in formal advances in string theory (1). It is possible to delineate the precursory works dealing with the possibility of a braneworld universe (2), and nowadays there is a great variety of alternative models dealing with several aspects regarding braneworlds. Motivated by a comprehensive program regarding gravity and black strings on braneworld scenarios, and subsequent generalizations probing extra-dimensional features (3-10), some gravitational aspects concerning black strings, aris- ing from braneworld models with variable brane tension, are introduced and widely investigated. In order to analyze a conceivable gravitational effect, arising genuinely from the brane variable tension, we analyze the corrections on the black string time-dependent horizon, in such a sce- nario. This formalism provides manageable models and their possible ramifications into some aspects of gravity in this context, cognizable corrections, and physical effects as well. Besides the black string behavior being sharply modified by the variable tension brane localized at y ¼ 0 (the extra dimension is denoted by y), unexpected addi- tional terms in a Taylor expansion of the metric along the extra dimension are elicited. This Taylor expansion regards the black string horizon behavior along the extra dimen- sion. Taking into account a variable tension brane, this expansion involves the covariant derivatives of the brane tension—besides its Lie derivative along the extra dimen- sion likewise. Such expansion, for instance, was used in (11) to investigate the gravitational collapse of compact objects in braneworld scenarios.