Summary and Info
This thesis deals with essentially four different topics within general relativity: pedagogical techniques for illustrating curved spacetime, inertial forces, gyroscope precession and optical geometry. Concerning the pedagogical techniques, I investigate two distinctly different methods, the dual and the absolute method.Contents:1. Introduction2. An introduction to Einstein's gravity3. Making illustrations4. Making models5. Spacetime visualization6. Inertial forces7. Gyroscope precession8. Optical geometry9. Conclusion and outlookComments on the research papers:10. A spherical interior dual metric11. The absolute visualization12. Kinematical invariants13. Lie transport and Lie differentiationPapers:I. Embedding spacetime via a geodesically equivalent metric of euclidean signatureII. Visualizing curved spacetimeIII. Inertial forces and the foundations of optical geometryIV. An intuitive approach to inertial forces and the centrifugal force paradox in general relativityV. A covariant formalism of spin precession with respect to a reference congruenceVI. Gyroscope precession in special and general relativity from basic principlesVII. Generalizing optical geometryIX. Optical geometry across the horizon
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