KTH, Department of Mechanics, Stockholm, Sweden


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.)

Lars Söderholm


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.