General Expressions for Measurable Geometric and Kinematic Quantities in Curved Spacetime
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Authors
Lebedev, Dmitri
Date
Type
thesis
Language
eng
Keyword
General Relativity , Geometry , Astrophysics
Alternative Title
Abstract
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented in full generality, which is applicable to any orientation of observers and light rays. An expansion for the geometrical exponential map is established and used to form an expression for the physical distance between an observer and a nearby object within its extended local frame. Curvature effects on such distances, velocities, and accelerations are made explicit and appear in general tensorial form. The concepts of Fermi frames on timelike worldlines and the Fermi-Walker derivative are discussed in detail and used throughout; and in examining the meaning of relative stationarity between timelike observers, the Fermi-Walker derivative is established from first principles through physically meaningful consideration. A generalized type of Taylor expansion is provided for tensors of any rank in a covariant form. Expressions for the optically based angular diameter distance and luminosity distance are provided in general forms, and the reciprocity theorem is discussed and verified. Effect of the Weyl tensor component of curvature on volume deformation is demonstrated (contrary to the common claim in the opposite), and a generalized version of the geodesic deviation equation, applicable to extreme relative motion, is provided.
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Attribution 4.0 International
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.