  The focussing optics of NuSTAR have enabled high signal-to-noise spectra to
be obtained from many X-ray bright Active Galactic Nuclei (AGN) and Galactic
Black Hole Binaries (BHB). Spectral modelling then allows robust
characterization of the spectral index and upper energy cutoff of the coronal
power-law continuum, after accounting for reflection and absorption effects.
Spectral-timing studies, such as reverberation and broad iron line fitting, of
these sources yield coronal sizes, often showing them to be small and in the
range of 3 to 10 gravitational radii in size. Our results indicate that coronae
are hot and radiatively compact, lying close to the boundary of the region in
the compactness - temperature diagram which is forbidden due to runaway pair
production. The coincidence suggests that pair production and annihilation are
essential ingredients in the coronae of AGN and BHB and that they control the
shape of the observed spectra.

High Energy Astrophysical Phenomena