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Title: Generalised Tolman-Bondi cosmologies and Kerr metric atoms
Author: Gair, J. R.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2002
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Abstract:
In the first part, we derive and investigate a family a cosmological models, which are a generalisation of the Lemaítre-Tolman-Bondi solution. The models are spherically symmetric and are composed of collisionless particles, with each particle possessing angular momentum about the symmetry centre. The radial motion and the magnitude of the angular momentum is the same for every particle on a given spherical shell, but there are particles moving in every tangential direction at each point. In this way the net angular momentum on a given spherical shell is zero and spherical symmetry is maintained. The solution to Einstein's equations describing the family of spacetimes with this matter content is derived in mass and proper time coordinates. The general properties of these models are discussed, including matching conditions and conditions to avoid shell crossing. The self-similar solutions in this family are derived and their physical properties described. A family of radiation spacetimes is obtained by taking the null limit of the particle solutions, i.e. by replacing the particles with photons. These generalize the Vaidya solution. Finally, by taking the limit in which every shell of particle has the same areal radius, a generalisation of the Kantowski-Sachs spacetime is found. These latter solutions may be envisaged as the surface of a cylinder, in which every circular cross section represents a two-sphere. The equation of relative motion of the matter shells along the surface of the cylinder is derived and discussed. The metrics in the general family represent inhomogeneous solutions with only a tangential pressure. This has application as a simple model cosmology or to describe the evolution of regions within our universe, for instance the recollapse of material to form a black hole within an expanding background. The spherical angular momentum model applies to many areas of astrophysics, including the modelling of clusters. These solutions provide a general relativistic description for such situations. The second part of the thesis concerns a problem on the much smaller, atomic scale. The Kerr-Newman solution in general relativity describes the spacetime around a charged and rotating black hole. If the limit G (r) 0 of this solution is taken, flat space is obtained, but the electromagnetic field remains. This electromagnetic field has many interesting properties, and possesses both a charge and magnetic moment. The G (r) 0 limit is appropriate for objects on an atomic scale. In oblate spheroidal coordinates, the Schrödinger equation separates for the electric part of the field, and the Klein-Gordon and Dirac equations separate for the full electromagnetic field. Of particular interest is the latter case, as it describes the interaction of two particles with magnetic moments.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.599270  DOI: Not available
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