Schwarzschild coordinates beyond the event horizon

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SUMMARY

The discussion focuses on the Schwarzschild coordinates of a black hole, specifically addressing their validity in relation to the event horizon. It is established that while the coordinates can be written down for the Schwarzschild black hole, they are singular at the event horizon, where the metric components ##g_{tt}## become zero and ##g_{rr}## approach infinity. This indicates that Schwarzschild coordinates are not valid at the event horizon, but they can be used both inside and outside of it.

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Afonso Campos
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We can write down the metric of the Schwarzschild black hole in Schwarzschild coordinates.

Which aspect of the metric in Schwarzschild coordinates indicates that the coordinates are only valid outside the event horizon?
 
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Afonso Campos said:
Which aspect of the metric in Schwarzschild coordinates indicates that the coordinates are only valid outside the event horizon?
None - they're valid inside the event horizon as well as outside. They are singular at the event horizon (##g_{tt}## is zero and ##g_{rr}## goes to infinity) so aren't valid there.
 
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Got it! Thanks!
 

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