PROGRAM IN GENERAL RELATIVITY

Since 1996, I have regularly been offering a sequence of four advanced level courses in the Physics Department, (the first course on tensors is also co-listed as a mathematics course). The sequence normally begins in a Spring term, and currently the first course on general relativity is offered in the Fall term of an odd number year, with the other two courses being offered in successive terms. The three relativity courses are intended for doctoral level students in physics interested in doing research in general relativity, but are also of interest to advanced students in theoretical physics and astronomy. The Graduate School requires all doctoral candidates to have three 600 level courses as a minimum course requirement, and these courses may be used to meet this requirement.

I do not follow a specific text in the three relativity courses, the books: The Classical Theory of Fields (Course of Theoretical Physics - Volume 2), by L.D. Landau and E.M. Lifshitz; and Relativistic Astrophysics, (Volume1, Stars and Relativity), by Ya. B. Zel'dovich and I.D. Novikov, are recommended references. These courses are topically oriented in which the prinicipal ideas / results are carefully described, with the routine calculations being outlined, but not repeated if they are readily available in the usual texts.

There are no written examinations, and grading is based on problem sets that are due at regular intervals. Class participation is encouraged, and questions are welcome.

PHYS 649 = MATH 649 : APPLICATIONS OF TENSOR ANALYSIS
Introduction to tensor analysis, Gaussian differential geometry, and Riemannian geometry. A working knowledge of vector methods is assumed, and numerous physical applications in electrodynamics and special relativity are included. This course is intended to cover the tensor-theoretic preliminaries for PHYS 650.

PHYS 650 : GENERAL RELATIVITY - I
Basic foundations and principles of general relativity, derivation of the Einstein field equations and their consequences, the linearized theory, the Bel-Petrov classification of the curvature tensors, derivation of the Schwarzschild solution: and the four basic tests of general relativity.

PHYS 651 : GENERAL RELATIVITY - II
The elementary theory of degenerate stars; physics of gravitational collapse; derivations of the axially symmetric solutions of Weyl, Kerr, and Vaidya; the Penrose process and Hawking's area theorem; the 'no hair' theorem; Penrose's cosmic censorship conjecture; Hawking radiation; and the observational evidence for black holes.

PHYS 652 : GENERAL RELATIVITY - III
Basic properties of the 'standard model' of Friedmann-Lemaître-Robertson-Walker; the Einstein-de Sitter models; group-theoretic methods in relativistic cosmology including derivations of the 'standard model,' the Gödel model; the inflation paradigm; the problem of dark matter; and observational cosmology.

 

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