- #1
Passionflower
- 1,543
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In "Gravitation" - Misner, Thorne, Wheeler, the second part of formula 25.38 (first part describes the proper time left till the singularity) seems to suggest it describes some kind of coordinate time left. But the question is what exactly?
Here is the formula:
[tex]
t={\it 2M}\, \left( -2/3\, \left( {\frac {r}{{\it 2M}}} \right) ^{3/2}
-2\,\sqrt {{\frac {r}{{\it 2M}}}}+\ln \left( \left( \sqrt {{\frac {r
}{{\it 2M}}}}+1 \right) \left( \sqrt {{\frac {r}{{\it 2M}}}}-1
\right) ^{-1} \right) \right)
[/tex]
Now this seems to behave well but not close to 2M. For instance if we graph for 2M=1 we get:
Time left actually becomes zero at around 1.203325645.
Perhaps I am doing something wrong or is there a good explanation?
For comparison proper time left:
Here is the formula:
[tex]
t={\it 2M}\, \left( -2/3\, \left( {\frac {r}{{\it 2M}}} \right) ^{3/2}
-2\,\sqrt {{\frac {r}{{\it 2M}}}}+\ln \left( \left( \sqrt {{\frac {r
}{{\it 2M}}}}+1 \right) \left( \sqrt {{\frac {r}{{\it 2M}}}}-1
\right) ^{-1} \right) \right)
[/tex]
Now this seems to behave well but not close to 2M. For instance if we graph for 2M=1 we get:
Time left actually becomes zero at around 1.203325645.
Perhaps I am doing something wrong or is there a good explanation?
For comparison proper time left:
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