Contributions to the relativistic mechanics of continuous media

  title={Contributions to the relativistic mechanics of continuous media},
  author={J{\"u}rgen Ehlers},
  journal={General Relativity and Gravitation},
  • J. Ehlers
  • Published 1 December 1993
  • Mathematics
  • General Relativity and Gravitation
This is a translation from German of an article originally published inProceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature, Nr. 11, 1961 (pp. 792–837) (printed by Franz Steiner and Co, Wiesbaden), which is Paper IV in the series “Exact Solutions of the Field Equations of General Relativity Theory” by Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt and Rainer K. Sachs. The translation has been carried out by G. F. R. Ellis (Department of Applied… 

Exact solutions of the field equations of the general theory of relativity

The series of papers now being reprinted as Golden Oldies were the product of Pascual Jordan’s strong relativity group at Hamburg University in the immediate postwar period, initially comprising

Relativistic Continuum Mechanics: A 20th Century Adventure

Relativity theory as understood by Einstein is a true Twentieth century development. After the introduction of the four-dimensional version of special relativity by Minkowski and that of

Contributions of K. Gödel to relativity and cosmology

K Gδdel published two seminal papers on general relativity theory and its application to the study of cosmology. The first examined a non-expanding but rotating solution of the Einstein field

83 years of general relativity and cosmology: progress and problems

This paper considers the evolution of the relation between gravitational theory and cosmology from the development of the first simple quantitative cosmological models in 1917 to the sophistication

On the non-attractive character of gravity in f(R) theories

In General Relativity without a cosmological constant a non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditions are assumed

On the non-attractive character of gravity in f(R) theories

In General Relativity without a cosmological constant a non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditions are assumed

A Generalized Method for Constructing Perfect-Fluid Solutions of Einstein's Equations

Using a 3-dimensional formulation of general relativity for non-empty spacetimes admitting a non-null Killing field, a transformation for generating new non-vacuum solutions of Einstein’s equations

Editorial note to: On the Newtonian limit of Einstein’s theory of gravitation (by Jürgen Ehlers)

We give an overview of literature related to Jurgen Ehlers’ pioneering 1981 paper on Frame theory—a theoretical framework for the unification of general relativity and the equations of classical

Kinematics and dynamics off(R) theories of gravity

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalisedf(R) theories of



An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation

Kurt Gödel became interested in general relativity theory while he and Einstein were both on staff of the Institute for Advanced Studies in Princeton, and saw a lot of each other (Ref. 25, p.7, Ref.

The Meaning of Relativity

In 1921, five years after the appearance of his comprehensive paper on general relativity and twelve years before he left Europe permanently to join the Institute for Advanced Study, Albert Einstein

The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid

The considerations of the first paper of this series are modified so as to be consistent with the special theory of relativity. It is shown that the inertia of energy does not obviate the necessity

On Gauss' theorem and the concept of mass in general relativity

The present communication is concerned with the extension to general relativity theory of the well-known theorem of Gauss on the Newtonian potential, viz., that the total flux of gravitational force

Relativistic Rankine-Hugoniot Equations

In Part I of this paper the stress energy tensor and the mean velocity vector of a simple gas are expressed in terms of the Maxwell-Boltzman distribution function. The rest density ρ0, pressure, p,

Space-time continua of perfect fluids in general relativity

When the expressions proposed by Einstein for the components of the energy-momentum tensor of matter in the state of a perfect fluid are substituted in the field equations of general relativity,

Necessity of Singularities in the Solution of the Field Equations of General Relativity

The Friedmann solution of the field equations of general relativity predict the expansion of the universe from a singular instant in time. This paper considers the behavior of universes which are

Thermodynamics and cosmology

A new type of cosmological history which includes large-scale entropy production is proposed. These cosmologies are based on a reinterpretation of the matter-energy stress tensor in Einstein's

Gravitational waves in general relativity III. Exact plane waves

Plane gravitational waves are here defined to be non-flat solutions of Einstein’s empty spacetime field equations which admit as much symmetry as do plane electromagnetic waves, namely, a 5-parameter

Relativistic Cosmology. I

The paper presents some general relations obtaining in relativistic cosmology. It appears from these that a simple change over to anisotropy without the introduction of spin does not solve any of the