  The partition function of gravitons with Casimir-type boundary conditions is
worked out. The simplest box that allows one to achieve full analytical control
consists of a slab geometry with two infinite parallel planes separated by a
distance d. In this setting, linearized gravity, like electromagnetism, is
equivalent to two free massless scalar fields, one with Dirichlet and one with
Neumann boundary conditions, which in turn may be combined into a single
massless scalar with periodic boundary conditions on an interval of length 2d.
When turning on a chemical potential for suitably adapted spin angular
momentum, the partition function is modular covariant and expressed in terms of
an Eisenstein series. It coincides with that for photons. At high temperature,
the result provides in closed form all subleading finite-size corrections to
the standard (gravitational) black body result. More interesting is the
low-temperature/small distance expansion where the leading contribution to the
partition function is linear in inverse temperature and given in terms of the
Casimir energy of the system, whereas the leading contribution to the entropy
is proportional to the area and originates from gravitons propagating parallel
to the plates.
