No abstract

On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special-and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, in the second part, material-independent equilibrium conditions are discussed. While in literature, at least if one works in the theory of irreversible thermodynamics assuming a Riemann space-time structure, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space-time geometries the necessary equilibrium conditions of vanishing entropy supply and entropy production are exploited and, afterwards, supplementary conditions are assumed which are motivated by the requirement that thermodynamic equilibrium quantities have to be determined uniquely.

The model of a. thin massive shell is investigated in the framework of gravitational theories with fourth-order derivatives. The corresponding jump conditions are derived, and their possible consequences for structure and motion of the matter sources are shortly discussed. The results are compared with the conditions obtained in General Relativity Theory. Schalenmodelle in Cfravitationstheorien mit htiheren AbleitungenI n h a l t s u b e r s i c h t . Es werden masse-behaftete diinne Schalenmodelle im Rahmen von Gravitationstheorien vierter Ordnung untersucht. Die entsprechenden Sprungbedingungen werden abgeleitet und die Bewegung der Materiequellen kurz diskutiert. Die Resultate werden mit den in der Allgemeinen Relativitiitstheorie erhaltenen verglichen.

In relativistic theory of irreversible thermodynamical processes near equilibrium, generally a series of assumptions is made having, in particular, the consequence that the temperature vector is a Killing vector. We show that, in contrast to usual approaches, in equilibrium (i) the temperature vector can also be a conformal Killing vector, (ii) as an implication of the Killing property of the temperature vector, most assumptions made can be derived, without restricting the matter configuration to a perfect fluid, (iii) for non-vanishing rotation of the fluid, the heat-flow is unequal to zero, (iv) for vanishing acceleration of the fluid the Friedmann radiation cosmos is the only physically significant solution of Einstein's equations and (v) the equilibrium conditions are of the Cattaneo form such that a causal propagation of temperature can be expected.