In 
-dimensional Lorentzian
space 
,
the light cone 
is defined to be the subset consisting of all vectors
 |
(1)
|
whose squared (Lorentzian) norm 
is identically zero:
 |
(2)
|
Alternatively, 
is the collection of all lightlike vectors in 
.
The decomposition of 
into Lorentzian space of signature 
leads to a natural decomposition of such a vector 
into its 
component and its 
-subvector 
. Using this notation, the squared
norm of 
can be expressed as
 |
(3)
|
whereby one can also define the light cone to be the collection of all vectors 
satisfying
 |
(4)
|
This particular perspective makes natural the distinction between positive and negative lightlike vectors.
The open subset of 
formed by the interior of the light cone consists of all timelike
vectors; the open subset formed by the exterior of 
consists of all vectors which are spacelike.
