Volume element for null hypersurface

[sadegh4137]

hi every body
Consider we have a null hypersurface. how we can calculate volume element on it?

 

[Bill_K]

Consider we have a null hypersurface. how we can calculate volume element on it?

You can define a volume element on a null surface in terms of an affine parameter along the null generators. But it won't be unique.

 

[sadegh4137]

how can i do it?
is it possible to introduce a book or an article for more detail?
I studied Advanced General Relativity By Eric Poisson. In this book, there is a few material.

 

[George Jones]

Section 3.2 from "A Relativist`s Toolkit" by Poisson might be useful; draft version at

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

 

[Bill_K]

Section 3.2 from "A Relativist`s Toolkit" by Poisson might be useful; draft version at

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

Yes, very good! See Eq (3.2.7)

 

[sadegh4137]

exactly i Studied this section of Poisson's book
, but here he defined a directed volume element
I don't know how to calculate volume element exactly.

 

[Bill_K]

exactly i Studied this section of Poisson's book
, but here he defined a directed volume element
I don't know how to calculate volume element exactly.

Then this should have been stated immediately. It shouldn't take us 6 posts to discover what it is you are actually looking for, and the fact that you already had an answer in hand and were dissatisfied with it.

 

[sadegh4137]

My question is clear. I want to find a way to calculate volume element of null hypersurface. Isn't it?
In Poisson's book,there is a way to find out directed volume element.
In this book, there is a little description about volume element of null hypersurface.
OM, It was better to tell what I studied Poisson before and have a question. you're right.