  The acceleration parameter defined through the local volume expansion is
negative for a pressureless, irrotational fluid with positive energy density.
In the presence of inhomogeneities or anisotropies the volume expansion rate
results from averaging over various directions. On the other hand, the
observation of light from a certain source in the sky provides information on
the expansion along the direction to that source. If there are preferred
directions in the underlying geometry one can define several expansion
parameters. We provide such definitions for the case of the Tolman-Bondi
metric. We then examine the effect of a localized inhomogeneity on the
surrounding cosmological fluid. Our framework is similar in spirit to the model
of spherical collapse. For an observer in the vicinity of a central
overdensity, the perceived local evolution is consistent with acceleration in
the direction towards the center of the overdensity, and deceleration
perpendicularly to it. A negative mass leads to deceleration along the radial
direction, and acceleration perpendicularly to it. If the observer is located
at the center of an overdensity the null geodesics are radial. The form of the
luminosity distance as a function of the redshift is consistent with
acceleration for a certain range of redshifts.
