Multipole moments of axisymmetric spacetimes

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case. Using Herberthson’s method we also develop a method for finding a static axisymmetric spacetime with arbitrary prescribed multipole moments, subject to a specified convergence criteria. This method has, in general, a step where one has to find an explicit expression for an implicitly defined function. However, if the number of multipole moments are finite we give an explicit expression in terms of power series. Acknowledgements I would like to thank my supervisor Magnus Herberthson for his support and much inspiration. I would also like to thank my second supervisor Brian Edgar for giving me many suggestions and correcting my language. I would like to thank Bengt-Ove Turesson for many fruitful ideas and giving me references to Sturmfels’ work on solutions to algebraic equations. Thanks to Ingemar Eriksson, Fredrik Andersson, and Johan Thim for reading the manuscript. December 21, 2005 (11:17)