Light cone coordinates
Encyclopedia
In relativity
, light-cone coordinates is a special coordinate system where two of the coordinates, x+ and x- are null
coordinates and all the other coordinates are spatial. Call them
.
Assume we're working with a (d,1) Lorentzian signature.
Instead of the standard coordinate system
,
with
we have
with
, 
and 
.
Both x+ and x- can act as "time" coordinates.
One thing nice about light cone coordinates is that the causal structure is partially included into the coordinate system itself.
A boost in the tx plane shows up as
, 
, 
. A rotation in the ij-plane only affects 
. The parabolic transformations show up as 
, 
, 
. Another set of parabolic transformations show up as 
, 
and 
.
Light cone coordinates can also be generalized to curved spacetime in general relativity. Sometimes, calculations simplify using light cone coordinates. See Newman-Penrose formalism
.
Light cone coordinates are sometimes used to describe relativistic collisions, especially if the relative velocity is very close to the speed of light. It's also used in the light cone gauge
of string theory.
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
, light-cone coordinates is a special coordinate system where two of the coordinates, x+ and x- are null
Null
-In computing:* Null , a special marker and keyword in SQL* Null character, the zero-valued ASCII character, also designated by NUL, often used as a terminator, separator or filler* Null device, a special computer file that discards all data written to it...
coordinates and all the other coordinates are spatial. Call them
.Assume we're working with a (d,1) Lorentzian signature.
Instead of the standard coordinate system
,with
we havewith
, and .Both x+ and x- can act as "time" coordinates.
One thing nice about light cone coordinates is that the causal structure is partially included into the coordinate system itself.
A boost in the tx plane shows up as
, , . A rotation in the ij-plane only affects . The parabolic transformations show up as , , . Another set of parabolic transformations show up as , and .Light cone coordinates can also be generalized to curved spacetime in general relativity. Sometimes, calculations simplify using light cone coordinates. See Newman-Penrose formalism
Newman-Penrose Formalism
The Newman-Penrose Formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for General Relativity. Their notation is an effort to treat General Relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR.The NP formalism is itself a...
.
Light cone coordinates are sometimes used to describe relativistic collisions, especially if the relative velocity is very close to the speed of light. It's also used in the light cone gauge
Light cone gauge
In theoretical physics, light cone gauge is an approach to remove the ambiguities arising from a gauge symmetry. While the term refers to several situations, a null component of a field A is set to zero in all cases.-Gauge theory:In gauge theory, light-cone gauge refers to the condition A^+=0...
of string theory.