I'm looking at the extension of the Schwarzschild metric using Kruskal coordinates defined as ##u'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r+t)}{4M}}} ##(adsbygoogle = window.adsbygoogle || []).push({});

##v'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r-t)}{4M}}} ##

In these coordinates the metric is given by:

##ds^{2}=-\frac{16M^{3}}{r}e^{-\frac{r}{2M}}(du'dv'+dv'du')+r^{2}d\Omega^{2}##

Question

The text says (lecture notes on GR, Sean M.Carroll)##u'## and ##v'## are null coordinates in the sense that their partial derivatives ##\frac{\partial}{du'} ,\frac{\partial}{dv'} ## are null vectors.

I've had a google on can't seem to find anything on this.

I have no idea what he means here and what is meant by##\frac{\partial}{du} ##.

I have never heard of a partial derivative of a coordinate..

Once I know what this is, do I do the same check as you do for normal vectors classification - checking whether the pseudo scalar product is ##>0##, ##<0## etc?

Thanks.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How to classify coordinate as S-L,Null,T-L?

Loading...

Similar Threads - classify coordinate Null | Date |
---|---|

I Transforming to local inertial coordinates | Feb 22, 2018 |

I Using Black Holes to Time Travel Into the Future | Feb 4, 2018 |

I Coordinate singularity at Schwarzschild radius | Dec 12, 2017 |

I Evaluating metric tensor in a primed coordinate system | Dec 5, 2017 |

I In which field can relativity theory be classified? | Mar 11, 2016 |

**Physics Forums - The Fusion of Science and Community**