# Light-cone/Null Coordinates

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.

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

$$x^+=\frac{1}{\sqrt{2}}(x^0+x^1) \qquad,\qquad x^-=\frac{1}{\sqrt{2}}(x^0-x^1)$$ Both $x^+$ and $x^-$ are world lines of light. In a way both of them are time coordinates, though none of them are not 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.