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Article: Vacuum solutions of the gravitational field equations in the brane world model
Title  Vacuum solutions of the gravitational field equations in the brane world model 

Authors  
Keywords  Physics  nuclear physics 
Issue Date  2004 
Publisher  American Physical Society. The Journal's web site is located at http://prd.aps.org 
Citation  Physical Review D (Particles and Fields), 2004, v. 69 n. 6, p. 064020:111 How to Cite? 
Abstract  We consider some classes of solutions of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario, in which our Universe is a threebrane embedded in a higher dimensional spacetime. The vacuum field equations on the brane are reduced to a system of two ordinary differential equations, which describe all the geometric properties of the vacuum as functions of the dark pressure and dark radiation terms (the projections of the Weyl curvature of the bulk, generating nonlocal brane stresses). Several classes of exact solutions of the vacuum gravitational field equations on the brane are derived. In the particular case of a vanishing dark pressure, the integration of the field equations can be reduced to the integration of an Abel type equation. A perturbative procedure, based on the iterative solution of an integral equation, is also developed for this case. Brane vacuums with particular symmetries are investigated by using Lie group techniques. In the case of a static vacuum brane admitting a oneparameter group of conformal motions, the exact solution of the field equations can be found, with the functional form of the dark radiation and pressure terms uniquely fixed by the symmetry. The requirement of the invariance of the field equations with respect to the quasihomologous group of transformations also imposes a unique, linear proportionality relation between the dark energy and dark pressure. A homology theorem for the static, spherically symmetric gravitational field equations in the vacuum on the brane is also proven. 
Persistent Identifier  http://hdl.handle.net/10722/43424 
ISSN  2004 Impact Factor: 5.156 
ISI Accession Number ID 
DC Field  Value  Language 

dc.contributor.author  Harko, TC  en_HK 
dc.contributor.author  Mak, MK  en_HK 
dc.date.accessioned  20070323T04:45:26Z   
dc.date.available  20070323T04:45:26Z   
dc.date.issued  2004  en_HK 
dc.identifier.citation  Physical Review D (Particles and Fields), 2004, v. 69 n. 6, p. 064020:111  en_HK 
dc.identifier.issn  05562821  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/43424   
dc.description.abstract  We consider some classes of solutions of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario, in which our Universe is a threebrane embedded in a higher dimensional spacetime. The vacuum field equations on the brane are reduced to a system of two ordinary differential equations, which describe all the geometric properties of the vacuum as functions of the dark pressure and dark radiation terms (the projections of the Weyl curvature of the bulk, generating nonlocal brane stresses). Several classes of exact solutions of the vacuum gravitational field equations on the brane are derived. In the particular case of a vanishing dark pressure, the integration of the field equations can be reduced to the integration of an Abel type equation. A perturbative procedure, based on the iterative solution of an integral equation, is also developed for this case. Brane vacuums with particular symmetries are investigated by using Lie group techniques. In the case of a static vacuum brane admitting a oneparameter group of conformal motions, the exact solution of the field equations can be found, with the functional form of the dark radiation and pressure terms uniquely fixed by the symmetry. The requirement of the invariance of the field equations with respect to the quasihomologous group of transformations also imposes a unique, linear proportionality relation between the dark energy and dark pressure. A homology theorem for the static, spherically symmetric gravitational field equations in the vacuum on the brane is also proven.  en_HK 
dc.format.extent  130756 bytes   
dc.format.extent  122136 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  application/pdf   
dc.language  eng  en_HK 
dc.publisher  American Physical Society. The Journal's web site is located at http://prd.aps.org  en_HK 
dc.rights  Physical Review D (Particles and Fields). Copyright © American Physical Society.  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject  Physics  nuclear physics  en_HK 
dc.title  Vacuum solutions of the gravitational field equations in the brane world model  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=05562821&volume=69&issue=6&spage=064020:1&epage=11&date=2004&atitle=Vacuum+solutions+of+the+gravitational+field+equations+in+the+brane+world+model  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.doi  10.1103/PhysRevD.69.064020  en_HK 
dc.identifier.hkuros  90074   
dc.identifier.isi  WOS:000221258900052   