A lightlike four-vector 
is one whose four-vector
norm has square 
.
The square of the four-vector norm is the self-pairing of a four-vector under
the more general Lorentzian inner product 
on 
-dimensional Lorentzian
space with 
and metric signature 
in the negative-first convention. In this more general
environment, the Lorentzian inner product
of two vectors 
and 
has the form
 |
whereby one defines a vector 
to be lightlike precisely when 
.
Lightlike vectors are sometimes called null vectors. The collection of all lightlike vectors in a Lorentzian space (e.g., in the Minkowski space of special relativity) is known as the light cone. One often distinguishes positive lightlike vectors from negative lightlike vectors.
