2003/05/31 by Edward Anderson, Reza Tavakol
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Nonlinear Waves and Solitons #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/20/23/l01
published as Class.Quant.Grav. 20 (2003) L267-L276 · Replaced with final version: minor changes to text; references added. Journal-ref added
openalex publication_date 2003/10/24 · arxiv created 2003/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We reformulate the Shiromizu, Maeda and Sasaki (SMS) braneworlds within the framework of the five-dimensional Einstein equations. In many applications of the braneworld Einstein field equations, the Weyl term is attributed to the bulk, thus splitting the non-Einsteinian terms into 'bulk' and 'brane' terms. Here by employing standard geometrical identities, we show that such a split is non-unique, since they get mixed up in different formulations. An important consequence of this non-uniqueness is that even though the full brane-bulk systems in all such formulations are completely equivalent, important differences can arise were one to truncate different formulations by throwing away the associated 'bulk' terms. This is particularly likely to be the case in more general anisotropic/inhomogeneous settings with non-AdS bulks, in which the common truncation of the SMS (which throws away the Weyl term) would not coincide with the full system. We emphasize that rather than providing support for any particular truncation, these differences show clearly the dangers of using any truncated equations and provide a strong argument in favour of studying the full brane–bulk system. The different formulations we provide also permit different ways of approaching the full brane–bulk system which may greatly facilitate its study. An example of this is the second-order nature of the formulations given here as opposed to SMS's formulation which is third order.