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

TitleVacuum solutions of the gravitational field equations in the brane world model
Authors
KeywordsPhysics - nuclear physics
Issue Date2004
PublisherAmerican 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. 064020:1-11 How to Cite?
AbstractWe 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 three-brane embedded in a higher dimensional space-time. 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 one-parameter 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 Identifierhttp://hdl.handle.net/10722/43424
ISSN
2004 Impact Factor: 5.156
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHarko, TCen_HK
dc.contributor.authorMak, MKen_HK
dc.date.accessioned2007-03-23T04:45:26Z-
dc.date.available2007-03-23T04:45:26Z-
dc.date.issued2004en_HK
dc.identifier.citationPhysical Review D (Particles and Fields), 2004, v. 69 n. 6, p. 064020:1-11en_HK
dc.identifier.issn0556-2821en_HK
dc.identifier.urihttp://hdl.handle.net/10722/43424-
dc.description.abstractWe 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 three-brane embedded in a higher dimensional space-time. 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 one-parameter 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.extent130756 bytes-
dc.format.extent122136 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/pdf-
dc.languageengen_HK
dc.publisherAmerican Physical Society. The Journal's web site is located at http://prd.aps.orgen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsPhysical Review D (Particles and Fields). Copyright © American Physical Society.en_HK
dc.subjectPhysics - nuclear physicsen_HK
dc.titleVacuum solutions of the gravitational field equations in the brane world modelen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0556-2821&volume=69&issue=6&spage=064020:1&epage=11&date=2004&atitle=Vacuum+solutions+of+the+gravitational+field+equations+in+the+brane+world+modelen_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1103/PhysRevD.69.064020en_HK
dc.identifier.hkuros90074-
dc.identifier.isiWOS:000221258900052-

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