A four-vector 
is said to be lightlike if its four-vector
norm satisfies 
.
One should note that the four-vector norm is nothing more than a special case of the more general Lorentzian inner product 
on Lorentzian 
-space with metric signature 
: In this more general environment, the 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 draws distinction between lightlike vectors which are positive and those which are negative.
