Curved spaces admiting solutions to twistor equations
<p>This thesis comprises three sections. In the first, real space-times admitting a solution to the two-index twistor (Killing spinor) equation are constructed and the separability properties of solutions to zero rest-mass field equations within these space-times are derived. In addition condi...
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| Format: | Thesis |
| Language: | English |
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1984
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| Summary: | <p>This thesis comprises three sections. In the first, real space-times admitting a solution to the two-index twistor (Killing spinor) equation are constructed and the separability properties of solutions to zero rest-mass field equations within these space-times are derived. In addition conditions for differential relations between components of opposite helicity are derived.</p>
<p>In the second section class of half algebraically-special spaces is investigated, a class which may be characterised as those admitting a certain partial two-index twistor (Killing spinor). A formalism based on their structure as a two-dimensional family of flat null two-planes is developed and used to provide an explicit integration of the curvature equations, to discuss Hertz-type potentials for zero rest-mass fields and to examine a class of Einstein-Maxwell spaces and their perturbations. </p>
<p>In the third section we examine the relation between the space of solutions to the twistor equation restricted to a general space--like two-surface of spherical topology (two-surface twistor space) and its dual. This is then used to discuss the nature of the local embedding of the two-surface in a space conformally related to complex Minkowski space.</p> |
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