2016/02/29 by V. D. Ivashchuk
Mathematics · Physics and Astronomy · #Ansatz #Black Holes and Theoretical Physics #Brane cosmology #Cosmology and Gravitation Theories #Covariant transformation #Dynamical billiards #Geometric Analysis and Curvature Flows #Limit (mathematics) #Product (mathematics) #Quantum #Scalar (mathematics) #hep-th
paper · pdf · doi:10.1140/epjc/s10052-016-4138-1
31 pages, Latex, no figures, based on a talk at Int. Session-Conf. of the Sect. of Nucl. Phys. of PSD RAN "Physics of Fundamental Interactions", April 12-15, 2016, JINR, Dubna; few typos are eliminated, some references are updated and reordered
openalex publication_date 2016/05/01 · arxiv created 2016/05/25 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a gravitational model in dimension D with several forms, l scalar fields and a Λ -term. We study cosmological-type block-diagonal metrics defined on a product of an 1-dimensional interval and n oriented Einstein spaces. As an electromagnetic composite brane ansatz is adopted and certain restrictions on the branes are imposed the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDW equation are found in the limit of the formation of the billiard walls. These solutions reduce the problem to the so-called quantum billiard in (n + l -1) -dimensional hyperbolic space. Several examples of quantum billiards in the model with electric and magnetic branes, e.g. corresponding to hyperbolic Kac–Moody algebras, are considered. In the case n=2 we find a set of basis asymptotic solutions to the WDW equation and derive asymptotic solutions for the metric in the classical case.