ON THE FOUNDATIONS OF RELATIVISTIC ENERGY MECHANICS
Abstract
The En theory of general relativity is shown to yield a general mechanics of continuous media under the assumption that the momentum-energy tensor admits a unique time-like eigenvector. Physical interpretations of the governing equa tions are derived, together with constitutive re lations for general and isotropic materials. It turns out that the mechanics can always be viewed as describing the flow of rest-energy. Invariant requirements for the existence of a stress poten tial are obtained, the satisfaction of which leads to a decomposition and partial evaluation of the rest-energy. The Einstein field equations are shown to imply the existence and uniqueness of an intrinsic energy density for any material medium (intrinsic immutable mass). The usual procedure of adding conditions to the Einstein theory in order to obtain an analogous intrinsic quantity is thus unnecessary. The path density, which defines the intrinsic energy, is shown to be path independent in an appropriate sense if the stresses admit a stress potential. This suggests a decomposition of the generalized stresses and leads to a funda mental differential relation on the trajectories of the energy flux. Natural definitions of in trinsic temperature and intrinsic entropy density are direct consequences of the fundamental dif ferential relation and lead to generalized thermo dynamic descriptions which include the effects of gravitational radiation.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1963
- Accession Number
- AD0408034
Entities
People
- Dominic G. Edelen
Organizations
- RAND Corporation