  The gravitational interaction is scale-free in both Newtonian gravity and
general theory of relativity. The concept of self-similarity arises from this
nature. Self-similar solutions reproduce themselves as the scale changes. This
property results in great simplification of the governing partial differential
equations. In addition, some self-similar solutions can describe the asymptotic
behaviors of more general solutions. Newtonian gravity contains only one
dimensional constant, the gravitational constant, while the general relativity
contains another dimensional constant, the speed of light, besides the
gravitational constant. Due to this crucial difference, incomplete similarity
can be more interesting in general relativity than in Newtonian gravity.
Kinematic self-similarity has been defined and studied as an example of
incomplete similarity in general relativity, in an effort to pursue a wider
application of self-similarity in general relativity. We review the
mathematical and physical aspects of kinematic self-similar solutions in
general relativity.
