Black Hole question?

Question

I've heard of something called like a Swartzchild radius, and I think it has something to do with the distace to the event horizon, but I'm not sure. Can someone explain exactly what it is, it's importance, and what we get from it?

Answer 1

They are slightly different...

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a characteristic radius associated with every mass. It is the radius for a given mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity. The term is used in physics and astronomy, especially in the theory of gravitation, general relativity.

In general relativity, event horizon is a general term for a boundary in spacetime, defined with respect to an observer, beyond which events cannot affect the observer. Light emitted from beyond the horizon can never reach the observer, and anything that passes through the horizon from the observer's side is never seen again. A black hole is surrounded by an event horizon, for example.

The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body that fits inside this radius. (A rotating black hole operates slightly differently.) The Schwarzschild radius of an object is proportional to the mass. For the mass of the Sun it is approximately 3 km, and for that of the Earth about 9 mm. For a black hole created by the collapse of a star (which has a mass above the Chandrasekhar limit) the lower limit is about 4 km.

Answer 2

Yea, you're on the right track. The schwarzchild radius is the radius at which a certain mass would collapse into a black hole if you could fit all of it's mass into that radius. It is derived from something called the schwarzchild metric from general relativity... it's quite mathematically intense but basically schwarzchild found it by solving one of Einstein's equations.

Here's an example of how it works.
R=2Gm/c^2

where R is the schwarzchild radius
G is the gravitational constant
m is the mass of your object
c is the speed of light.
2G/c^2 = 1.48×10−27 m/kg.

If you wanted to turn a 1 liter (aka 1 kg) bottle of water into a black hole you could use this to see how small of a space you'd need to fit it into.

R=(1.48*10^-27)m/kg*(1)kg
R=1.48*10^-27 meters

Really really tiny! Hope this gives you a better idea of things!

Answer 3

This is the radius at which, if a given mass were shrunk smaller then this, the object would collapse into a black hole.

Each mass would have a different Swartzchild radius.

Swartzchild radius= (2Gm)/c^2

G being the gravitational constant, m being the mass, and c being the speed of light in a vacuum.

The best way to think of this is in terms of escape velocity. What would the power of gravity have to be for not even light to escape.

Answer 4

i'm not sure with this but i think the Schwartzschild radius is commonly called 'Event Horizon' an imaginary border above the surface of a black hole below spacetime is that much bended that nothing can get out anymore.

So i would say its the same.