The Universe Revealed is my attempt to discuss more thoroughly the main questions that we humans should ask about our existence, our universe and our place in it. These are mostly my thoughts on science, religion and philosophy as it applies to the...
A Schwarzschild Black Hole is a spherical boundary that's called an event horizon, which is located at the Schwarzschild radius. This is strictly a mathematical convenience. It's not an actual surface. The key here is that any object that's not rotating and not charged with a mass that fits into (is less than the) Schwarzschild radius will be a back hole. We need a equation to express what happens to a test particle falling into the event horizon. How is its time affected?
To define the black hole we use the Schwarzschild metric equation: c^2 dτ^2 = (1 - rs/r) c^2dt^2 - (1 - rs/r)^-1 dr^2 - r^2 (dθ^2 + sin θ dφ^2)
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where τ is the proper time (time measured by a clock moving along the same world line with test particle)
c is the seed of light
t is the time measured by a stationary clock that's distant from the black hole
r is the radial coordinate (which is the circumference divided by 2π of a sphere centered around the black hole
θ is the longitude (in radians)
rs is the Schwarzschild radius of the black hole. This is related to the mass M by rs = 2GM/c^2 where G is the gravitational constant.
These Schwarzschild radii are very small. The Earth's is 8.9 mm and Sun's is only 3.0 km. This rs/r ratio is tiny and only becomes significant when it's used for a black hole or something like a neutron star. You could think of it this way: If you took all the mass in an object like a star and squashed it down into sphere where the escape velocity would be the speed of light that would be the Schwarzschild radius for that object. That's what the event horizon would look like for that object if it were the core of a large star after a supernova.
Karl Schwarzschild found this exact solution to the Einstein field equations and published this in 1916 but he died shortly afterwards from a disease because of his service in the German army in WW I.
This Schwarzschild metric is only valid outside the black hole. It doesn't work for inside it.
What does all this mean? It means that a poor fool who falls into a black hole is going to be ripped apart but won't feel anything. He'll think that time has stopped or slowed down to a crawl. The guy at a distance will think that the guy falling into the black hole just disappeared.
