On Maximal Extensions of the Vaidya Metric
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Authors
Aboelhassan, Sheref
Date
Type
thesis
Language
eng
Keyword
General Relativity , Black Holes , Maximal Extensions , Israel's coordinates , Dynamical Black Holes , The Vaidya Metric
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Abstract
The common ``Eddington-Finkelstein-like" coordinates are not complete, thus not covering the entirety of the Vaidya manifold. The main aim of this thesis is to create and analyze three maximal extensions of the Vaidya metric, which is a spherically symmetric solution to the Einstein field equations for the energy momentum tensor of pure radiation in the high-frequency approximation. This metric is necessary for various applications, such as describing the exterior geometry of a radiating star in astrophysics and studying possible formation of naked singularities in the geometry of spacetime. We look into the Israel metric, which was an important step in finding maximal extensions of the Vaidya manifold, though it was given via coordinate transformations. We obtain the Israel coordinates in a constructive manner without recourse to coordinate transformations. By recognizing that each maximal extension can be differentiated by the mass function, we develop three mass functions, one for each extension. We then inspect the qualitative characteristics of the three mass models and the surfaces of constant radius. The first extension is formed by starting with a Schwarzschild vacuum solution, which then has `outflux' of radiation for a period of time before the `outflux' is turned off to get another (with a less mass) Schwarzschild vacuum solution. The second extension is accomplished by adding `influx' of radiation to an already existing Schwarzschild vacuum region, and the final spacetime is essentially Schwarzschild vacuum (the mass now being larger than the initial Schwarzschild). The third extension is constructed by choosing a mass function that creates an exploding Vaidya metric that eventually changes to an imploding Vaidya metric. The most noteworthy element of these maximal extensions is that they are null geodesically complete, which we assess by solving the radial null geodesics equation and forming the Penrose conformal diagram for each extension.
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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.
Attribution-NonCommercial-NoDerivs 3.0 United States
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.
Attribution-NonCommercial-NoDerivs 3.0 United States