Volume element for null hypersurface

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Discussion Overview

The discussion revolves around the calculation of the volume element for a null hypersurface, exploring theoretical approaches and references to literature in the context of general relativity.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • Some participants propose defining a volume element on a null surface using an affine parameter along the null generators, noting that this definition may not be unique.
  • One participant expresses a desire for further resources, specifically mentioning "Advanced General Relativity" by Eric Poisson as a study reference.
  • Another participant suggests Section 3.2 from "A Relativist's Toolkit" by Poisson as potentially useful, providing a link to the draft version.
  • A participant indicates familiarity with the suggested section but notes that it defines a directed volume element rather than a general volume element, expressing uncertainty about how to calculate the latter.
  • There is a critique regarding the clarity of the original question, suggesting that the participant should have stated their prior knowledge and dissatisfaction with existing explanations sooner.
  • One participant reiterates their question about calculating the volume element of a null hypersurface, emphasizing the limited description provided in Poisson's book.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the calculation of the volume element, with some expressing confusion and others providing references that may not fully address the question.

Contextual Notes

The discussion highlights limitations in the existing literature regarding the volume element of null hypersurfaces, particularly the distinction between directed and general volume elements.

sadegh4137
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hi every body
Consider we have a null hypersurface. how we can calculate volume element on it?
 
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sadegh4137 said:
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.
 
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.
 
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.
 
George Jones said:
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)
 
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.
 
sadegh4137 said:
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.
 
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.
 

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