  We study the collective excitations of a neutral atomic Bose-Einstein
condensate with gravity-like $1/r $ interatomic attraction induced by
electromagnetic wave. Using the time-dependent variational approach, we derive
an analytical spectrum for monopole and quadrupole mode frequencies of a
gravity-like self-bound Bose condensed state at zero temperature. We also
analyze the excitation frequencies of the Thomas-Fermi-gravity (TF-G) and
gravity (G) regimes. Our result agrees excellently with that of Giovanazzi {\em
et al}. [Europhysics Letters, {\bf 56}, 1 (2001)], which is obtained within the
sum-rule approach. We also consider the vortex state. We estimate the
superfluid coherence length and the critical angular frequencies to create a
vortex around the $ z $-axis. We find that the TF-G regime can exhibit the
superfluid properties more prominently than the G-regime. We find that the
monopole mode frequency of the condensate decreases due to the presence of a
vortex.
