  For static matter in a gravitational field, different conventions for
equilibrium local temperature exist in the classic physics literature. We
illustrate the difference between two popular conventions using black-body
radiation in a spherically symmetric gravitational potential. Equilibrium
temperatures defined by the "Landau frame" or "Eckart frame" prescriptions most
commonly used in relativistic fluid dynamics do not satisfy the
statistical-mechanical relation $1/T=dS/dE$.
