Inverse Compton Scenarios for the TeV Gamma-Ray Emission of the Galactic Centre

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.