Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole.

Suppose we define the quantity $$u=t- v$$ where $$dv/dr= 1/(1-r_{s}/r)$$ where $r_s$ is the Schwarzschild radius. What is the $u$ as observed by the emitter? I just need a definition of $u_e$. I have problems identifying the quantities as measured by an observer at large $r$ and that of the emitter. Would I be right at least to say that $$t_{e}=\tau$$ the proper time? Many thanks.


In fact, I've been told that

$$du_o/d\tau=du_e/d\tau$$

Why is it?


My apologies for leaving out a subscript $e$ in the question. It has been added.

share|cite|improve this question
    
What are $u$ and $v$? Whose proper time is $\tau$? I think we need more background to the setup of your question. – Nathan Reed Mar 9 '13 at 21:58
    
@NathanReed: $u,v$ are defined in the question...! I don't know whose proper time that is, unfortunately. I am only given the metric! I have already included all the info I know... – Sad confused person Mar 9 '13 at 22:26
    
No, $u, v$ are not defined in the question. :) You've given a couple of relationships between $u, v$ and the coordinates $r, t$, but I still have no idea what you intend $u, v$ to actually mean. And how can you not know whose proper time you're talking about? It's your question, after all. Sorry, but you're going to have to do a better job of asking what you want to know. Where is all of this coming from - a textbook, a homework problem? Give us more context. – Nathan Reed Mar 9 '13 at 22:29
    
@NathanReed: :) It is taken from some old notes. Let's assume the proper time is that of the emitter and the observer located at a constant large r. – Sad confused person Mar 9 '13 at 23:07
    
If you define $u$ by your first two equations, then $u,r$ form a system of Outgoing Eddington Finkelstein coordinates. $u$=const describes an outgoing null ray, which I guess in your picture is the path which represents a light pulse emitted by the emitter and received by the observer who sits fixed at large $r$. Like Nathan though, I'm not sure whose proper time we're talking about. – twistor59 Mar 10 '13 at 8:57

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.