On the variability of the GeV and multi-TeV gamma-ray emission from the
  Crab Nebula
  Recently the AGILE $\gamma$-ray telescope has reported the enhanced
$\gamma$-ray emission above 100 MeV from the direction of the Crab Nebula
during a period of a few days. This intriguing observation has been confirmed
by the Fermi-LAT telescope. This emission does not show evidences of pulsations
with the Crab pulsar. It seems that it originates at the shock region created
as a result of the interaction of the pulsar wind with the nebula. We propose
that such variable $\gamma$-ray emission originate in the region behind the
shock when the electrons can be accelerated as a result of the reconnection of
the magnetic field compressed by the decelerating pulsar wind. The natural
consequence of such interpretation is the prediction that the Crab Nebula
$\gamma$-ray spectrum produced by electrons as a result of the inverse Compton
scattering of soft radiation to multi-TeV energies should also show synchronous
variability on the time scales as observed at GeV energies by the AGILE and
Fermi-LAT telescopes. We calculate how the end of the IC component of the Crab
Nebula $\gamma$-ray spectrum should look like during the quiescent and the
flare GeV $\gamma$-ray emission. We conclude that the variability of the
multi-TeV $\gamma$-ray spectrum from the Crab Nebula might in principle be
responsible for the differences between the spectral features reported by the
HEGRA and HESS Collaborations at the multi-TeV energies.
