Mathematics – Logic
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........8j&link_type=abstract
Thesis (PH.D.)--STANFORD UNIVERSITY, 1995.Source: Dissertation Abstracts International, Volume: 56-10, Section: B, page: 5549.
Mathematics
Logic
2
General Relativity, Cosmology, Gravitational Lensing, Spacetime Metric
Scientific paper
To understand astronomical observations of objects at large distances, it is essential to have a model of the cosmological spacetime metric. The Universe on average seems well-described by the uniform-density FLRW models, but with metric perturbations possible on all scales. The first part of the thesis is devoted to a method for solving the gravitational field equations for these perturbations. It gives an expression in terms of a pseudo-Newtonian gravitational potential, which is valid for an almost arbitrary range of matter-density fluctuation amplitudes. The matter-density field is assumed to be known, and the metric perturbations are assumed to be scalar-type, that is, with no "gravitomagnetic" (vector) or gravitational-wave (tensor) components. The application of the expression for the potential is illustrated by simple calculations of deflection and redshift for a light ray passing an isolated, static mass-point, and compared to the corresponding Newtonian (or thin-lens) calculations. Fractional changes to the deflection are essentially insignificant; however for high emitter redshifts the correction to the Newtonian redshift perturbation can be on the order of 10%, both perturbation values being about 1: 10 ^6 of the unperturbed value due to the cosmological expansion. Finally, on a separate topic, the second part of the thesis deals with the geodesic motion of test particles in Godel's universe, and its similarity to the motion of charged particles in a uniform magnetic field.
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