Open Access Te Herenga Waka-Victoria University of Wellington
thesis_access.pdf (829.03 kB)
Download file

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

Download (829.03 kB)
posted on 2021-11-10, 23:45 authored by Cropp, Bethan

In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline


Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Master of Science

Victoria University of Wellington Item Type

Awarded Research Masters Thesis



Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research


Visser, Matt