A four-vector 
is said to be spacelike 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 
-dimensional 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 spacelike precisely when 
.
Geometrically, the collection of all spacelike vectors lie in the open subset of 
formed by the exterior of the light
cone.
