  The nature of the massive object at the Galactic Center (Sgr A$^{*}$) is
still unclear even if various observational campaigns led many authors to
believe that our Galaxy hosts a super-massive black hole with mass $M\simeq
2.6\times 10^6$ M$_{\odot}$. However, the black hole hypothesis, which
theoretically implies a luminosity $\simeq 10^{41}$ erg s$^{-1}$, runs into
problems if one takes into account that the observed luminosity, from radio to
$\gamma$-ray wavelengths, is below $10^{37}$ erg s$^{-1}$. In order to solve
this blackness problem, alternative models have been recently proposed. In
particular, it has been suggested that the Galactic Center hosts a ball made up
by non-baryonic matter (e.g. massive neutrinos and anti-neutrinos) in which the
degeneracy pressure of fermions balances their self-gravity. Requiring to be
consistent with all the available observations towards the Galactic Center
allows us to put severe astrophysical constraints on the neutrino ball
parameters. The presence of such an object in the Galactic Center may be
excluded if the constituent neutrino mass $m_{\nu}$ is $\ut> 24$ keV, while if
$m_{\nu}\ut< 24$ keV observations can not give a definite answer.
