A model for relativistic heat transport
Abstract
The classical Fourier law for heat conduction implies infinite velocity of propagation; attempts to remedy this by adding a term do not provide a satisfactory description. In order to investigate the proper relativistic description of heat transport a model is studied consisting of a cloud of fixed material particles, which exchange energy by electromagnetic radiation. After eliminating the filed quantities one is left with an integral equation for the temperature of the particles as a function of time and space. By solving this equation exactly it is verified that nothing propagates faster than c. However, when the equation is approximated by a differential equation of first order in time, precursors are introduced, which precede the wave front over a distance of the order of the mean free path of a photon. When this differential equation is cut off after the second order space derivative, the velocity c disappears and the classical equation is obtained. A more detailed summary of the results is given in section 5.
- Publication:
-
Physica
- Pub Date:
- March 1970
- DOI:
- 10.1016/0031-8914(70)90231-4
- Bibcode:
- 1970Phy....46..315V