Albert Einstein (1879 - 1955) |
spacetime diagram for two black holes colliding to become one |
Einstein with Tagore |
This class will provide an overview of the theory of general relativity,
Einstein's theory of relativistic gravity, as well as some basic applications, including
at least the solar-system tests of gravitational theories,some of the more interesting properties of
black holes and gravitational waves, along with some surveys of
cosmology.
This class will not completely prepare you for research
in this area:
it will be an overview with insufficient depth for that purpose.
| |
The first third to half of the course will focus primarily on the basic structure of the theory, with relevant physical motivation and insight thrown in along the way, and also provide a reasonable introduction to the needed mathematics. You do NOT need to already know more physics and mathematics than is described in the Prerequisite section just below. The major applications will come after that, although perhaps some discussion of motions around spherical stars, and weak gravitational waves will come in the earlier sections. | |
| I assume you have a good foundation in standard undergraduate physics:
classical mechanics, electromagnetism, and the usual junior-level special relativity. Also you should have a
mathematics background in calculus, differential equations, and linear algebra.
The mathematics of general relativity is
differential geometry, but I am not assuming you have had
any studies on that before: we will spend a good fraction of the first
portion of the course learning the relevant differential geometry. An extended/advanced course in special relativity is NOT necessary. Only the basic ideas of spacetime, 4-vectors, Minkowski diagrams, etc. are needed from special relativity; our time will mostly be concerned with questions involving gravitational fields in 4-dimensional spacetime. |
Textbooks and Syllabus:
From here on, the handouts consider various specific applications to physical systems.
Exams and Homework Assignments: There will be two
examinations, currently scheduled for 21 March and 27 April,
but no final examination.
In addition, there will be (more or less) weekly homework assignments,
with solutions posted after they have been turned in.
The grader for
the course is (Stephen) Keith Sanders. If you wanted to speak with him, note that he usually attends class, but you could
also email him for a meeting time and place.
Homework Assignments | Due Date | Homework Solutions | |
HW #1, | due 27 Jan. | Solutions for HW #1 | |
HW #2, extended | due 3 Febr. | Solutions for HW #2 | |
HW #3, | due (Monday) 15 February. | Solutions for HW #3 | |
HW #4, | due (Monday) 22 February. | Solutions for HW #4 | |
HW #5, | due (Wednesday) 2 March. | Solutions for HW #5 | |
HW #6, | due (Wednesday) 9 March. | Solutions for HW #6 | |
An Exam on Monday, 21 March, 2016 You may bring any personally-written material with you, or my handouts for this class. | Solutions are available here. | ||
HW #7, | due (Monday) 28 March. | Solutions for HW #7 | |
HW #8, | due (Monday) 11 April. | Solutions for HW #8 | |
HW #9, | due (Wednesday) 20 April. | Solutions for HW #9 | |
Exam 2 (Take Home) is due on Wednesday, 4 May, 2016 It is due at the beginning of class that day. You may NOT consult with any humans other than myself; | Solutions are here |
Homework assignments and Solutions are pdf-files, except when occasionally
there will be an html-file for a portion of the solutions.
Solutions will
be made available once the assignments have been turned in.
Homework is
DUE at the beginning of the class period on the due date!
There are many modern software packages to perform tensor
calculations.
I
prefer the program grtensor, which is described in more
detail in this linked webpage.
After you have a reasonably-good understanding of how the
process works, I see no reason why you shouldn't have an algebraic
computing system do the work for you.
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