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dc.contributor.authorFazio, Jordan
dc.date.accessioned2019-09-30T14:10:18Z
dc.date.available2019-09-30T14:10:18Z
dc.identifier.urihttp://hdl.handle.net/10464/14535
dc.description.abstractIn Schwarzschild spacetime, the timelike geodesics are the trajectories of free, massive particles, orbiting a singularity at the origin r = 0. In this work we derive four scalar first integrals of timelike geodesics in Schwarzschild spacetime. Two of the first integrals, corresponding to energy and angular momentum, are well-known. The other two first integrals, an angular quantity and a temporal quantity, are not as well-known. Using the freedom to shift first integrals by a constant value we set a ‘zero-point’ for each of the four first integrals. By choosing a natural point on a non-circular trajectory such as a turning point or inertial point to set the zero-point value, the angular and temporal first integrals will correspond respectively to the angle and time of the chosen zero-point. We then take the Newtonian limit of the angular and temporal first integrals, and show that using a natural choice of zero-point they provide a generalization of the classical Laplace-Runge-Lenz (LRL) vector. We then evaluate the angular first integral for each type of timelike geodesic in Schwarzschild spacetime. In most cases we are able to choose a turning or inertial point to set a zero-point. For an unbound or asymptotic trajectory which falls into the singularity of the metric at r = 0, however, we find that we must take a different point, such as the point where the trajectory crosses the horizon at r = 2M, which we call the ‘horizon point.’ For the case of a precessing elliptic orbit we find that the angular first integral is multi-valued, with the zero-point jumping each time the trajectory crosses an apoapsis. It is found that the angular and temporal first integrals provide a relativistic generalization of the classical LRL vector, where we the first integrals correspond to a larger class of physically meaningful points compared to Newtonian orbits and where the LRL vector and angular and temporal first integrals may always correspond to the periapsis.en_US
dc.language.isoengen_US
dc.publisherBrock Universityen_US
dc.subjectSchwarzschilden_US
dc.subjectgeodesicen_US
dc.subjectLRLen_US
dc.subjectfirst integralen_US
dc.subjectGeneral Relativityen_US
dc.titleAn Analogue of the Laplace-Runge-Lenz Vector for Timelike Geodesics in Schwarzschild Spacetimeen_US
dc.typeElectronic Thesis or Dissertationen
dc.degree.nameM.Sc. Physicsen_US
dc.degree.levelMastersen_US
dc.contributor.departmentDepartment of Physicsen_US
dc.degree.disciplineFaculty of Mathematics and Scienceen_US
refterms.dateFOA2021-08-18T01:50:38Z


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