We study a spherically symmetric fluctuation of scalar dark matter in the c
osmos and show that it could be the dark matter in galaxies, provided that
the scalar field has an exponential potential whose overall sign is negativ
e and whose exponent is constrained observationally by the rotation velocit
ies of galaxies. The local space-time of the fluctuation contains a three-d
imensional spacelike hypersurface with a surplus of angle.