  The intense Compton cooling of ultra-relativistic electrons in the
Klein-Nishina regime in radiation dominated environments, such as that found in
the Galactic Centre, may result in radically different electron spectra than
those produced by Synchrotron cooling. We explore these effects and their
impact on the X-ray and gamma-ray spectra produced in electron accelerators in
this region in comparison to elsewhere in our galaxy. We discuss the broad-band
emission expected from the newly discovered pulsar wind nebula G 359.95-0.04
and the possible relationship of this X-ray source to the central TeV gamma-ray
source HESS J1745-290. Finally we discuss the possible relationship of the
Galactic Centre INTEGRAL source IGR J1745.6-2901 to the TeV emission.
