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Now I'm study the Schwarzschild geometry from "General Relativity (M.P. Hobson)".

Since the Schwarzschild metric has coordinate singularity at [tex]r=2M[/tex] so to remove this singularity they use the Eddington-Finkelstein coordinate,

first they begin with introduces new time parameter "p"

[tex]p=ct+r+2M ln\left |\frac{r}{2M}-1 \right |[/tex]

which is

[tex]dp=c dt+\frac{r}{r-2M}dr[/tex]

and they said that it's a null coordinate

after that , they said "since p is a null coordinate, which might be intuitively unfamiliar, it is common practice to work instead with the related timelike coordinate [itex]t^\prime[/itex]defined by"

[tex]ct^{\prime}=p-r=ct+2M ln\left |\frac{r}{2M}-1 \right |[/tex]

and it is a timelike coordinate which called "advanced Eddingtion-Finkelstein coordinate"

My question is how can I check that which coordinate are timelike nulllike or spacelike? Is there any explicit calculation to check this?

What wrong with the former coordinate which defined as p? Why should we use the new one instead?

Since the Schwarzschild metric has coordinate singularity at [tex]r=2M[/tex] so to remove this singularity they use the Eddington-Finkelstein coordinate,

first they begin with introduces new time parameter "p"

[tex]p=ct+r+2M ln\left |\frac{r}{2M}-1 \right |[/tex]

which is

[tex]dp=c dt+\frac{r}{r-2M}dr[/tex]

and they said that it's a null coordinate

after that , they said "since p is a null coordinate, which might be intuitively unfamiliar, it is common practice to work instead with the related timelike coordinate [itex]t^\prime[/itex]defined by"

[tex]ct^{\prime}=p-r=ct+2M ln\left |\frac{r}{2M}-1 \right |[/tex]

and it is a timelike coordinate which called "advanced Eddingtion-Finkelstein coordinate"

My question is how can I check that which coordinate are timelike nulllike or spacelike? Is there any explicit calculation to check this?

What wrong with the former coordinate which defined as p? Why should we use the new one instead?

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