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- Thread starter yenchin
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Garth

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Hiyenchin said:

The

[tex]r^\star = r + 2GM\ln\left|\frac{r}{2GM} - 1\right| [/tex].

The tortoise coordinate [itex]r^\star[/itex] approaches [itex] - \infty [/itex] as ''r'' approaches the Schwarzschild radius ''r'' = 2''GM''. It satisfies

[tex] \frac{dr^\star}{dr} = \left(1-\frac{2GM}{r}\right)^{-1} [/tex].

Watch the object fall towards the Schwarzschild radius at a constant

[tex]\frac{dr^\star}{dt}[/tex]

it 'slows right up', hence [itex]r^\star[/itex] is called the 'tortoise coordinate'.

Garth

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Oh... Thanks.

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George Jones

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Cexy said:

Because the Lie derivative is defined using a flow (of a vector field), like the flow of a stream in which the angler angles!

Regards,

George

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"it 'slows right up', hence r⋆ is called the 'tortoise coordinate'."

That coordinate was named tortoise coordinate due to the story of Achilles and the Tortoise, we know that the Tortoise think that Achilles wouldn't catch up itself forever, this case just like the observer of outside of blackhole who never saw anything fall into the blackhole, but in fact for a free falling observer who fall into the blackhole in a finite time. What saw outer of blackhole observer is just because he used the "Tortoise coordinate", that it means!

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"it 'slows right up', hence r⋆ is called the 'tortoise coordinate'."

That coordinate was named tortoise coordinate due to the story of Achilles and the Tortoise, we know that the Tortoise think that Achilles wouldn't catch up itself forever, this case just like the observer of outside of blackhole who never saw anything fall into the blackhole, but in fact for a free falling observer who fall into the blackhole in a finite time. What saw outer of blackhole observer is just because he used the "Tortoise coordinate", that it means!

Wow. Thanks for resurrecting my 5-year-old thread ;-)

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