Symmetries of Einstein’s Equations in Vacuum and Their Geodesics

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dc.contributor.advisorAkbar, Mohammad
dc.contributor.advisorBiewer, Michael
dc.contributor.committeeMemberDragovic, Vladimir
dc.contributor.committeeMemberKing, Lindsay
dc.contributor.committeeMemberLou, Yifei
dc.creatorKasmaie, Behshid
dc.date.accessioned2023-02-21T16:48:07Z
dc.date.available2023-02-21T16:48:07Z
dc.date.created2021-12
dc.date.issued2021-12-01T06:00:00.000Z
dc.date.submittedDecember 2021
dc.date.updated2023-02-21T16:48:08Z
dc.description.abstractThis thesis explores symmetries of vacuum Einstein equations that are static and at least axially symmetric, i.e., Ricci-flat Lorentzian geometries that admit a timelike Killing vector field and a closed spacelike Killing vector field among their isometries. We study symmetries of the geodesics in these spacetimes as well as symmetries of the system of Einstein equations describing such spacetimes. Geodesics in three dimensions have symmetries and associated conserved quantities absent in four and higher dimensions. We employ the socalled direct method for computing the conserved quantities. For the static axisymmetric system in vacuum, we found all symmetries of the system which enabled us to explain why one cannot obtain algebraic prescriptions for generating new solutions from old ones beyond those already known. Symmetries of the geodesics in spherical symmetry show that there is no general connection between cosmological constant and projective equivalence and that one can find an appropriate coordinate system where the effect of cosmological constant disappears from the bending angle, unlike in the static coordinates.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9580
dc.language.isoen
dc.subjectMathematics
dc.titleSymmetries of Einstein’s Equations in Vacuum and Their Geodesics
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.namePHD

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