The Schwarzschild metric

  • #1
167
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Homework Statement



The problem is I am wanting to know if the expression on the right hand side is dimensionless.

Homework Equations



[tex]ds^2 = (1 - \frac{2GM}{c^2 r})c^2 dt^2[/tex]

The Attempt at a Solution



Since the Schwarzschild radius is [tex]r = \frac{2GM}{c^2}[/tex] would I be right in saying that

[tex]\frac{2GM}{c^2 r}[/tex]

is dimensionless?
 

Answers and Replies

  • #2
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The Attempt at a Solution



Since the Schwarzschild radius is [tex]r = \frac{2GM}{c^2}[/tex] would I be right in saying that

[tex]\frac{2GM}{c^2 r}[/tex]

is dimensionless?

Yes, it is.
 
  • #3
vela
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Note that it would have to be if the formula is valid since you're subtracting that quantity from 1, which is dimensionless.
 
  • #4
131
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Of course it is. Note that sometime we write metric in this form:[tex]1-\frac{2GM}{r}[/tex]
just a matter of unit conventions.
 
  • #5
167
0
thanks every1
 
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