  Both diffuse high energy gamma-rays and an extended electron-positron
annihilation line emission have been observed in the Galactic Center (GC)
region. Although X-ray observations indicate that the galactic black hole Sgr
A$^*$ is inactive now, we suggest that Sgr A$^*$ can become active when a
captured star is tidally disrupted and matter is accreted into the black hole.
As a consequence the galactic black hole could be a powerful source of
relativistic protons. We are able to explain the current observed diffuse
gamma-rays and the very detailed 511 keV annihilation line of secondary
positrons by $p-p$ collisions of such protons, with appropriate injection times
and energy. Relativistic protons could have been injected into the ambient
material if the black hole captured a 50M$_\odot$ star at several tens million
years ago. An alternative possibility is that the black hole continues to
capture stars with $\sim$1M$_\odot$ every hundred thousand years. Secondary
positrons produced by $p-p$ collisions at energies $\ga 30$ MeV are cooled down
to thermal energies by Coulomb collisions, and annihilate in the warm neutral
and ionized phases of the interstellar medium with temperatures about several
eV, because the annihilation cross-section reaches its maximum at these
temperatures. It takes about ten million years for the positrons to cool down
to thermal temperatures so they can diffuse into a very large extended region
around the Galactic center. A much more recent star capture may be also able to
account for recent TeV observations within 10 pc of the galactic center as well
as for the unidentified GeV gamma-ray sources found by EGRET at GC. The
spectral difference between the GeV flux and the TeV flux could be explained
naturally in this model as well.
