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Suppose there is a narrow hole through the center of the earth. This hole passes through the Earth's Schwarzschild radius.

My question
Can light escape from Schwarzschild radius of Earth?

According to wikipedia the Schwarzschild radius of Earth is $8.87×10^{−3} m$. This seems to be long enough to be the wavelength.

Dale
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Blue Various
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2 Answers2

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Yes, light can escape. There is no event horizon at the Schwarzschild radius of the earth.

The Schwarzschild radius is just a characteristic length scale associated with a given mass. If an object with mass fits inside its Schwarzschild radius then it has an event horizon, but if an object is larger than its Schwarzschild radius then there is nothing peculiar that happens at the Schwarzschild radius.

Dale
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The quoted value of the Schwarzschild radius is the value you would get for a black hole having the same mass as the Earth.

For it to be a black hole, however, the entire mass would have to be inside a sphere of that radius. Since the Earth is so much larger, it can't have an event horizon, and light would have no trouble passing through the hypothetical hole through the Earth.

D. Halsey
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  • Thank you for the answer. In other words, the Earth do not have Schwarzschild radius ? – Blue Various Dec 25 '19 at 15:01
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    @Blue Various If the earth was a black hole (instead of the planet it is, but with the same mass), its size would be that Schwartzschild radius, and light could no escape. – Claudio Saspinski Dec 25 '19 at 15:39
  • @Claudio Saspinski Thank you for your comment. Say hello to (https://physics.stackexchange.com/questions/521264/schwarzschild-radius-of-a-black-hole-that-moves-linearly-at-a-constant-speed ) If you have time. – Blue Various Dec 25 '19 at 15:42
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    @Blue Various Whether Earth does, or does not, have a Schwarzschild radius is a matter of what is the precise definition of the term. According to the Wikipedia article, "it is a characteristic radius associated with every quantity of mass", as well as being the radius of the event horizon of a black hole. I guess, according to that, Earth would have one. However, I think it's very misleading to say that. – D. Halsey Dec 25 '19 at 15:51
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    @BlueVarious What do you mean? Anything with non-zero mass has a Schwarzschild radius. – PM 2Ring Dec 25 '19 at 15:52
  • @ PM 2Ring I used this term to mean "Anyone can't get out from the region inside the Schwarzschild radius." But this seems misunderstanding. – Blue Various Dec 25 '19 at 15:58
  • It depends on the definition but, The Earth also has a Schwarzschild radius, but one can escape even if one enter inside isn't it? But, for some reason, If all of the mass goes into it, the earth becomes a black hole. – Blue Various Dec 25 '19 at 16:07
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    @Blue Various “Anyone can't get out from the region inside the Schwarzschild radius” is incorrect. It should be “Anyone can't get out from the region inside an event horizon”. The Schwarzschild radius is just a characteristic length scale associated with a given mass. If an object with mass fits inside its Schwarzschild radius then it has an event horizon. I will add this to my answer above for clarity – Dale Dec 25 '19 at 16:40