bob jantzen
differential geometry, cosmology and relativity notes
if you find these notes useful please
contact me!
Over the years I wrote up (printing neatly by hand) a lot of notes of my
self-study or (post)-lecture notes on differential geometry, relativity and
gravitation, cosmology, gauge fields, etc. After 3 decades it occurred to me
that maybe someone else might find something useful in them, which would not
occur while they were sitting in a file cabinet. So in May-June 2006 I scanned
many of them and put them on-line.
Geometry of metric connections and GR, differential
forms,
variational approach to Einstein's equations
Bundles, Kaluza-Klein and gauge fields (UC Berkeley mid 1970s,
Chapel Hill 1979)
Rome theoretical physics lecture notes
- Special relativity notes (January, 1983?)
(11 pages)
- Cosmological models: four lectures (January 1984)
(35 pages)
- Cosmological models: a short course (too short) (Spring 1985)
(31 pages)
- Lecture notes on harmonics (May-June 1986)
(14 pages) Lifshitz 1
- Notes on the Lifshitz perturbation analysis (May 1984)
(24 pages) Lifshitz 2
- Symmetry breaking in cosmology (May 1987)
(SB: 40 pages) Lifshitz 3
-
- Appreciating the article "General Relativity and Kinetic Theory" by
Juergen Ehlers (May 1989)
(42 pages)
-
Introduction to Cosmological Models (March 1987)
(38 pages) incorporated into ICM1 the next year
-
- Some notes on Groups, Symmetries, Differential Geometry, and Splitting
Techniques in the Context of General Relativity
July 1995 [bundling of previous years notes]
- Rough notes written on a moving train (March 1990):
A Second Look at Tensors, Covariant Differentiation and Curvature
(SL: 12 pages)
- Curvilinear Coordinates and Curvature (January 1989)
(CCC: 4 pages)
- Introduction to Cosmological Models (ICM)
- Part I: orthogonal coordinates on flat or constant curvature
manifolds with metric, FRW geometry, simplest spacetime splittings,
Gaussian normal coords, intrinsic and extrinsic curvature (March
1987, January
1988)
(ICM1: 39 pages)
- Part II: Symmetries and Lie groups (March 1988)
(ICM2: 27 pages)
- Part III: Differential geometry, classical mechanics, matrix
groups, rigid body dynamics
(ICM3: 19 pages)
- Part IV: Fiber bundles, gauge groups (May 1988)
(ICM4: 20 pages)
- Part V: Anisotropic cosmological models, gravitational dynamics
(ICM5: 6 pages)
- Lie derivatives yet again (March 1991)
(LD: 4 pages)
- Spacetime splitting: Some notes on splitting techniques in general relativity (June 1994)
(SS: 14 pages) see below
- Symmetry breaking in cosmology (May 1987)
(SB: 40 pages) see above
- Some notes on splitting techniques in general relativity (June 1994)
(18 pages, plus some background notes)
Continued (June 1996)
(SS: 9 pages)
- Spacetime splitting '96: tensor harmonics and gravitoelectromagnetism
(SS96: 14 pages)
These were bundled with ICM1,2, SS1994, SB1987 for June 1996.
Villanova University Differential Geometry
Course/Independent Study Notes