Thermal equilibrium in a general gravitational field

In the absence of any appreciable gravitational field the conditions satisfied by the temperature of a medium having no thermal flow from one portion to another, are well known to be those of uniformity throughout the system. In the presence of a gravitational field, however, the conditions imposed at thermal equilibrium on the proper temperature -- as measured at different points of the medium by local observers -- are considerably more complicated, owing to the association of inertia and weight with all forms of energy and the consequent tendency for heat to flow from regions of higher to those of lower gravitational potential. Nevertheless, for the special case of static gravitational fields, these more complicated conditions have already been obtained,(1,2) and it is the purpose of the present article to investigate the conditions for thermal equilibrium in the general case of any kind of gravitational field