  We study lightlikeness preserving mappings from the $4$-dimensional Minkowski
spacetime $\mathcal{M}_4$ to itself under no additional regularity assumptions
like continuity, surjectivity, or injectivity. We prove that such a mapping
$\phi$ satisfies one of the following three conditions. (1) The mapping $\phi$
can be written as a composition of a Lorentz transformation, a multiplication
by a positive scalar, and a translation. (2) There is an event $r\in
\mathcal{M}_4$ such that $\phi(\mathcal{M}_4\setminus\{r\})$ is contained in
one light cone. (3) There is a lightlike line $\ell$ such that
$\phi(\mathcal{M}_4\setminus \ell)$ is contained in another lightlike line.
Here, a line that is contained in some light cone in $\mathcal{M}_4$ is called
a lightlike line. We also give several similar results on mappings defined on a
certain subset of $\mathcal{M}_4$ or the compactification of $\mathcal{M}_4$.
