I have a very basic question: what are the advantages of writing a metric in light-cone/null coordinates? Which extra insight do they provide?

I've looked in Caroll's "Spacetime and Geometry" and Wald's "General Relativity" but both concentrate more on the mathematical rather than intuitive/motivational side.

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    $\begingroup$ FWIW, light-cone coordinates separate most cleanly physical and gauge degrees of freedom in gauge theories. The price is breaking of manifest Lorentz covariance. $\endgroup$
    – Qmechanic
    Commented Jun 22, 2018 at 9:26

2 Answers 2


The advantage of writing the metric in null or double null coordinates are that the surfaces along which u or v are constant is lightlike


If @user46446 wanted to know about the light cone coordinates, then the following explanation might help a bit. Usual light-cone coordinates are in the form :

$$ x^+=\frac{1}{\sqrt{2}}(x^0+x^1) \qquad,\qquad x^-=\frac{1}{\sqrt{2}}(x^0-x^1) $$ Both $x^+$ and $x^-$ are world lines of light. In a way both of them are time coordinates, though neither of them are the usual time coordinate. All the particles move forward with the time and all of them fall inside the light cone. Light rays travel with $x^+=0$. The line element has the form $$ ds^2=-2dx^+dx^-+(dx^2)^2+(dx^3)^2 $$ Advanced Use: Light cone coordinates are most convenient when one wants to quantize the relativistic strings.

  • $\begingroup$ It is not accurate to say they are most "convenient" when quantising strings. Each quantisation method has its advantages. I would say light cone quantisation is simply the fastest way to the spectrum of the string, but it has its downsides too. $\endgroup$
    – JamalS
    Commented Jun 22, 2018 at 9:13
  • $\begingroup$ @JamalS agreed. That was a bit of a sloppy terminology. Thanks for correcting. $\endgroup$ Commented Jun 22, 2018 at 11:17

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