  Maps that preserve adjacency on the set of all invertible hermitian matrices
over a finite field are characterized. It is shown that such maps form a group
that is generated by the maps $A\mapsto PAP^{\ast}$, $A\mapsto A^{\sigma}$, and
$A\mapsto A^{-1}$, where $P$ is an invertible matrix, $P^{\ast}$ is its
conjugate transpose, and $\sigma$ is an automorphism of the underlying field.
Bijectivity of maps is not an assumption but a conclusion. Moreover, adjacency
is assumed to be preserved in one directions only.
  The main result and author's previous result [16] are applied to characterize
maps that preserve the `speed of light' on (a) finite Minkowski space-time and
(b) the complement of the light cone in finite Minkowski space-time.
