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Schwarzschild Black holes

  • Thread starter Brewer
  • Start date
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1. Homework Statement
Capture.jpg



2. Homework Equations
[tex]d\tau = dt\sqrt{1-\frac{r_s}{r}}[/tex]

and

[tex]\frac{dr}{d(ct)} = 1 - \frac{r_s}{r}[/tex]

3. The Attempt at a Solution
First of all I worked out the Schwarzschild radius to be [tex]2.964*10^4[/tex]m.

From this I plugged it into the first of the two equations above, along with [tex]d\tau = 30[/tex], and [tex]dt = 300[/tex] (years in both cases, but it'll cancel), and rearranged to give r as [tex]2.994*10^4[/tex]m, i.e. 300m outside the Schwarzschild radius.

From here I plugged these new numbers into the second equation that I've given in order to give [tex]\frac{dr}{d(ct)} = 0.01[/tex]. I assume that this means a fraction of c.

I'm not entirely convinced though. Can someone check what I've done please. Have I used the correct meanings of [tex]d\tau and dt[/tex]? Is the second equation that I've given the correct one to use? If not could someone point me in the right direction?

Thanks for anyone who helps out.
 

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