Gravity illustrated (Ph.D. Thesis)

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. Introduction 2. An introduction to Einstein's gravity 3. Making illustrations 4. Making models 5. Spacetime visualization 6. Inertial forces 7. Gyroscope precession 8. Optical geometry 9. Conclusion and outlook Comments on the research papers: 10. A spherical interior dual metric 11. The absolute visualization 12. Kinematical invariants 13. Lie transport and Lie differentiation Papers: I. Embedding spacetime via a geodesically equivalent metric of euclidean signature II. Visualizing curved spacetime III. Inertial forces and the foundations of optical geometry IV. An intuitive approach to inertial forces and the centrifugal force paradox in general relativity V. A covariant formalism of spin precession with respect to a reference congruence VI. Gyroscope precession in special and general relativity from basic principles VII. Generalizing optical geometry IX. Optical geometry across the horizon