Show simple item record

dc.contributor.authorPapallo, Giuseppeen
dc.contributor.authorReall, Harveyen
dc.date.accessioned2017-07-27T10:36:03Z
dc.date.available2017-07-27T10:36:03Z
dc.date.issued2017-08-15en
dc.identifier.issn2470-0010
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/265748
dc.description.abstractWe investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes “k-essence” like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.
dc.language.isoenen
dc.publisherAmerican Physical Society
dc.titleOn the local well-posedness of Lovelock and Horndeski theoriesen
dc.typeArticle
prism.number044019en
prism.publicationDate2017en
prism.publicationNamePhysical Review D - Particles, Fields, Gravitation and Cosmologyen
prism.volume96en
dc.identifier.doi10.17863/CAM.11518
dcterms.dateAccepted2017-07-12en
rioxxterms.versionofrecord10.1103/PhysRevD.96.044019en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2017-08-15en
dc.contributor.orcidPapallo, Giuseppe [0000-0002-3990-6761]
dc.contributor.orcidReall, Harvey [0000-0003-1363-6369]
dc.identifier.eissn2470-0029
dc.publisher.urlhttp://dx.doi.org/10.1103/PhysRevD.96.044019en
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idSTFC (ST/P000673/1)
pubs.funder-project-idSTFC (ST/L000636/1)
cam.issuedOnline2017-08-16en


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record