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
Author(s): Rickard Jonsson
Edition: Spacetime Edition
Publisher: Chalmers University of Technology and Goteborg University
Year: 2004
Language: English
Pages: 245
Front matter......Page 1
Contents......Page 5
1. Introduction......Page 8
2. An introduction to Einstein's gravity......Page 11
3. Making illustrations......Page 20
4. Making models......Page 25
5. Spacetime visualization......Page 30
6. Inertial forces......Page 34
7. Gyroscope precession......Page 36
8. Optical geometry......Page 38
9. Conclusion and outlook......Page 40
Comments on the research papers......Page 41
10. A spherical interior dual metric......Page 42
11. The absolute visualization......Page 46
12. Kinematical invariants......Page 56
13. Lie transport and Lie differentiation......Page 62
Bibliography......Page 68
I. Embedding spacetime via a geodesically equivalent metric of euclidean signature......Page 70
II. Visualizing curved spacetime......Page 103
III. Inertial forces and the foundations of optical geometry......Page 118
IV. An intuitive approach to inertial forces and the centrifugal force paradox in general relativity......Page 160
V. A covariant formalism of spin precession with respect to a reference congruence......Page 174
VI. Gyroscope precession in special and general relativity from basic principles......Page 201
VII. Generalizing optical geometry......Page 212
IX. Optical geometry across the horizon......Page 231
