Tolman temperature gradients in a gravitational field

Abstract

Tolman’s relation for the temperature gradient in an equilibrium self-gravitating general relativistic fluid is broadly accepted within the general relativity community. However, the concept of temperature gradients in thermal equilibrium continues to cause confusion in other branches of physics, since it contradicts naive versions of the laws of classical thermodynamics. In this paper we discuss the crucial role of the universality of free fall. We also provide an interesting pedagogical example for observers in a rotating cylinder and conclude by showing how thermodynamics emphasises the great distinction between gravity and other forces: we do so by presenting an argument given by Maxwell and applying it to an electro-thermal system, concluding with an reductio ad absurdum. Among other issues we shall show that Tolman temperature gradients could also (in principle) have been derived circa 1905—a decade before the development of full general relativity.