A covariant approach to gravitational lensing
Master Thesis
2004
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University of Cape Town
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Abstract
The main focus of this thesis is to study the properties of null geodesics in general relativistic models. This thesis is divided into two parts. In the first part, we introduce the (1+3)-covariant approach which will be used in our study of null geodesics and their applications to gravitational lensing. The dynamics of the null congruence can be better understood through the propagation and constraint equations in the direction of the congruence. Thus, we derive these equations after describing the geomentry of a ray. We also derive a general from of the null geodesic deviation equation (NGDE) which can be used in any given space-time. Various applications of this equation are studied, including its role in determining area-distance relations in an Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model. We also use the NGDE in deriving a covariant form of the angle of deflection, showing its versatile applications in gravitational lensing theory.
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Includes bibliography.
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De Swardt, B. 2004. A covariant approach to gravitational lensing. University of Cape Town.