A ug 2 00 3 A note on the thermodynamics of gravitational radiation

It is shown that linearized gravitational radiation confined in a cavity can achieve thermal equilibrium if the mean density of the radiation and the size of the cavity satisfy certain constraints. Is it possible, in principle, to confine gravitational radiation in a box, for a time long enough for it to achieve thermal equilibrium? This issue has been investigated before by various authors [1, 2, 3], not all of whom have arrived at the same conclusion. The purpose of this note is to pursue a particular line of thought which does not seem to have been looked at in earlier work. We argue that it is possible to thermalize gravitational radiation, starting from a non-equilibrium configuration, so long as certain constraints (to be discussed below) are satisfied. Let us begin by summarizing the arguments given by Smolin [1]. He showed, by considering various mechanisms of absorption of radiation by matter, that no realistic material is an efficient absorber of gravitational radiation, except over a narrow band of frequencies. These mechanisms include absorption of classical gravitational radiation by classical matter, ionization of atoms by gravitons, and phonon excitation. He concluded that a state of thermal equilibrium between radiation and matter cannot be reached in a finite time. e-mail address: [email protected] e-mail address: [email protected]