THERMODYNAMIC PROPERTIES OF $\gamma$--FLUIDS AND THE QUANTUM VACCUM

Abstract

The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state $p=(\gamma-1)\rho $, where $0 \le \gamma \le 2$ is a constant, has been investigated. Particular cases include: vacuum($p=-\rho $, $\gamma=0$), a randomly oriented distribution of cosmic strings ($p=-{1 \over 3} \rho $, $\gamma =2/3$), blackbody radiation ($p={1\over 3} \rho$, $\gamma =4/3$) and stiff matter ($p=\rho$, $\gamma=2$). Fluids with $\gamma <1$ become hotter when they expand adiabatically ($T\propto V^{1- \gamma}$). By assuming that such fluids may be regarded as a kind of generalized radiation, the general Planck's type form of the spectrum is deduced. As a limiting case, a new Lorentz invariant spectrum of the vacuum which is compatible with the equation of state and other thermodynamic constraints is proposed. Some possible consequences to the early universe physics are also discussed.