Other Notes
This page contains all the other notes I have made and uploaded.
Space-Time Transformations of Dispersive, Nonlinear Materials
(Lancaster Thesis)
Abstract:
Transformation optics is a powerful mathematical tool which has found extensive use through the design of metamaterials. One of the main areas of interest is that of producing cloaks, in both space and time. Although the effects of transformation optics have been studied for the cases of a dispersive background material and a nonlinear background material separately, they are yet to be studied on a material that is both dispersive and non- linear. This thesis considers this case and we provide a formalism for taking space-time transformations of materials whose dispersion is consistent to that of a one-pole resonator and whose nonlinearity is given by that of a Kerr medium. The problem is solved using both integral and differential methods, and the generation of non-trivial nonlinearities are shown explicitly. The methodology is set up in a way that the extension to higher powered nonlinearities is simple, and examples of how one would do that are provided throughout.
My Thoughts On Black Holes
This is some notes I made on my interpretation of gravity and black holes. I have tried to formulate the problem at the manifold level (i.e. without using coordinates). The main approach is to look at light cones and killing vector fields produced by your gravitating mass. I argue that what gravity does is cause a 'relative rotation' between these two. I have tried to provide as much background information as possible to make it accessible to beginner relativists (as I myself am).
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This is a work in progress.
