  We discuss energy densities in the strong-interaction limit of density
functional theory, deriving an exact expression within the definition (gauge)
of the electrostatic potential of the exchange-correlation hole. Exact results
for small atoms and small model quantum dots are compared with available
approximations defined in the same gauge. The idea of a local interpolation
along the adiabatic connection is discussed, comparing the energy densities of
the Kohn-Sham, the physical, and the strong-interacting systems. We also use
our results to analyze the local version of the Lieb-Oxford bound, widely used
in the construction of approximate exchange-correlation functionals.
