This page contains old material
from the last time this course was given. If you are interested in relativistic
continuum mechanics, please contact me.
Lars
Söderholm
INTRODUCTION TO RELATIVISTIC CONTINUUM MECHANICS
5C5117, 3 p, period 4, spring 1996
Relativistic conditions prevail when either temperatures
are so high, that the thermal energy is no longer negligible compared to
the rest mass energy or when the gravitational field is so strong, that
it cannot be described with Newtonian theory. The latter is the case in
the vicinity of and interior of neutron stars and black holes. Both situations
arise in cosmology. The case with relativistic temperatures also arises
in certain aspects of controlled thermonuclear fusion.
During the second half of spring 1996, I shall give a course on relativistic
continuum mechanics. It will be a natural continuation of the course on
special relativity, given by Bengt Enflo. In the course the basics of relativistic
continuum mechanics for elastic materials will be treated. (In continuum
mechanics any material which can be described with a Lagrangean is called
elastic. In particular, an elastic fluid is essentially the same as what
is traditionally called an ideal fluid.)
Outline of the course
Review of the 4-dimensional machinery of special
relativity, in particular motion of particles.
Relativistic kinematics of a continuum as mappings
The relativistic Lagrangean for an elastic continuum
and the corresponding equations of motion. Stress tensor, and all that
stuff.
Constitutive equations. Solids and fluids.
Relativistic fluid dynamics
Particle motion in a strong, spherically symmetric
gravitational field.
Stellar (solar) wind and accretion discs
There is no textbook covering all of the material, which is scattered
in the litterature. Notes will be given out during the lectures.
Some useful references
A.M. Anile, Relativistic fluids and magneto-fluids.
Cambridge University Press, Cambridge 1989.
J. Foster & J.D. Nightingale, A short course
in general relativity. Longman, London 1979.
L.D. Landau and E.M. Lifshitz, Fluid Mechanics. Pergamon,
Oxford, 1987.
S.L. Shapiro & S.A. Teukolsky, Black Holes, White
Dwarfs, and Neutron Stars. Wiley, New York, 1983.
Special relativity is needed as a background. The course will start
with a presentation of its four-dimensional formulation. Some experience
of non-relativistic continuum mechanics is of great value, but not absolutely
necessary.
There will be a
Meeting of introduction: Thursday 14 March
at 10.15 1996
in the Seminar room, Department of Mechanics.
The following meetings will be at 9.45 in the
small conference room in the department of Mechanics
Thursday 21 March; Relativistic kinematics of continua
Wednesday 10 April (Change of day!); Relativistic
dynamics of a particle and continua; Variational Principle
Thursday 18 April; Relativistic fluid dynamics
Thursday 25 April; Continuation; Physics on a curved
background.
Thursday 2 May; Stellar winds and accretion discs.
Please contact me if you are interested to take part in the course,
or have questions. My e-mail is lhs@mech.kth.se
and my phone number 790 7152.
Lars Söderholm
Last updated: December 22, 1998.