Mathematics of relativity (180707, 2 ov)
Joensuu, 20.2. - 10.3.2006
Professor Eric Lehman, University of Caen, France
Description of course content
The aim of the course is to give a simple presentation
of the mathematics needed to understand Einstein's theories of special
and general relativity and the Big Bang. In a first part, we study hyperbolic
geometry. In that geometry the squares of distances
| (x1 -
x2)2
+ (y1 -
y2)2
+ (z1 -
z2)2 |
|
are replaced by quantities computed with one minus sign instead
of one of the plus signs, like
| (x1 -
x2)2
+ (y1 -
y2)2-
(z1-
z2)2. |
|
The group of isometries is then replaced by the Poincaré
group and the Maxwell equations become simple. In a second part, we introduce
a riemannian manifold which describes the shape of space-time and we write
down Einstein's equation of gravitation. In the last part of the course
we give some explicit solutions of Einstein's equation. We show why the
cosmological constant is a mathematical necessity (it's value is a question
of physics) and how it is used in some cosmological models.
Recommended pre-knowledge: Elementary computations
with matrices: sum, linear combination, matrix product, matrix inversion.
Functions of several variables, partial derivatives.
Volume: 22 hours lectures/exercises + exam or
seminar presentation (2 ov)
Meeting schedule on weeks
8-10
| Dates |
Times |
Places |
| Mondays 20.2. and 6.3. |
12-14 |
M6, M6 |
| Tuesdays 21.2., 28.2. and 7.3. |
10-12, 16-18, 16-18 |
M13, M8, M8 |
| Wednesdays 22.2., 1.3. and 8.3. |
14-16 |
M8, M8, M8 |
Thursdays 23.2. and
9.3. (examination) |
12-14 |
M7, M7 |
| Fridays 24.2. and 3.3. |
12-14 |
M13, M13 |
Note: passing this course gives 1 ov of the English
language studies (in "common studies" of the Faculty of Science, old study
system).
Contact person: Martti.Pesonen@Joensuu.Fi