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.
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.
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.
