Talk:Schwarzschild radius

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Shouldn't the radius = square root ( 2GM/c^2) ???

No, see [1], [2], [3], etc. -- Tim Starling 04:25, Nov 18, 2004 (UTC)

Or, more simply, using dimensional analysis: $r\,$ is in meters ( $m\,$ ), so $2Gm/c^2\,$ must be in meters also. Let's see:

$G \to N\cdot m^2/kg^2\,$ , where $N\,$ is force = mass * acceleration = $kg\cdot m/s^2\,$ , so $G\,$ is in units of $(kg \cdot m/s^2) \cdot (m^2/kg^2)\,$ .

$m/c^2\,$ is in units of $kg/(m/s)^2 \to kg \cdot s^2/m^2$ .

So when combined $Gm/c^2\,$ is in units of $(kg \cdot m/s^2) \cdot (m^2/kg^2) \cdot (kg \cdot s^2/m^2)$ .

You can see directly that units of $kg\,$ and $s\,$ are equal in numerator and denominator, leaving $m^3/m^2 \to m\,$ (meters).

QED. Slowmover 20:23, 22 March 2006 (UTC)

1 Meaning for non-black holes?
2 Gravitational versus Schwarzchild radius
3 Low density black hole
4 Great Job on the Article
5 Removed incorrect claim

[edit] Meaning for non-black holes?

What is the physical meaning of an object's Schwarzschild radius when it is bigger than the radius? -- Myria 05:35, 29 December 2005 (UTC)

It means that this object is not a black hole. For an object to be a black hole, its mass needs to be concentrated in a radius less than its Schwarzschild radius. The same holds also for part of the object, so in theory it's possible that the whole object is not a black hole, but its inner part is a black hole. This subject is important to define the moment when a collapsing star becomes a black hole. This transition happens when its mass is concentrated in a radius that is equal to its Schwarzschild radius.

I'm not exactly where to put it, but when reading this article, it took me a while to figure out that a plain-English definition of the Schwartzchild radius makes more sense. The Schwartzchild radius is the radius for a given mass where, if that mass could be compressed to fit within that radius, no force could stop it from continuing to collapse into a singularity. Wouldn't it be nice to put such a definition in the article? Problem is that I'm not even remotely a physicist so I don't want to make the change myself.--MikeGinny 04:57, 30 June 2006 (UTC)

Giving this some thought. -- Slowmover 19:34, 30 June 2006 (UTC)

I think that one useful way to look at it is this: If you take an object with a particular mass, it has a certain amount of gravity, all of which has to exit through its surface. If you then squish the object into a smaller volume, the intensity of the gravitational field at the surface increases, and when you increase this surface gravity, you increase the escape velocity, the speed at which somethng has to be thrown with at the surface to have a chance of completely escaping. For a given mass M, the r=2M radius tells us how compact the material would have to be in order for this surface escape velocity to reach the critical situation of being equal to the nominal speed of light. John Michell did the calculations for this back in the Eighteenth Century, but when Isaac Newton's original ideas about light took a hammering, the idea became unfashionable and dropped out of sight until Karl Schwarzchild brought it back, more unambigiuously, in the context of Einstein's general theory of relativity, in the early Twentieth Century. ErkDemon 15:59, 29 December 2006 (UTC)

[edit] Gravitational versus Schwarzchild radius

I added a link to the hyperphysics sight because it distinguishes between a gravitational radius and a Scwarzschild radius. The distinction is an important one even though it is quite common to confuse the two.Lucretius 07:53, 15 January 2006 (UTC)

I subsequently removed the link because 'gravitaional radius' and 'Schwarzschild radius' are considered synonymous by the great majority of the scientific community.Lucretius 23:50, 15 January 2006 (UTC)

[edit] Low density black hole

below are the calculations for the mass and radius of a black hole with the density of water. The resulting mass is 135 million times the mass of the Sun. The radius is 400 million kilometres.

Calculations

[edit] Great Job on the Article

I just wanted to let the editors of this article know this article's far better than it was before; I didn't have a good idea of the Schwarzchild radius earlier, but it's clear now. This seems to be applicable to a lot of the physics articles in particular. Just wanted to point it out- thanks a lot for your contributions! Robinson0120 01:47, 17 January 2007 (UTC)

[edit] Removed incorrect claim

I removed this sentence:

The Schwarzschild radius of a sphere with a uniform density equal to the critical density is equal to the radius of the visible universe.

because it's not true--the Schwarzschild radius in this case is about 250 Gly, and the radius of the visible universe is about 50 Gly. There's certainly a meaningful relationship here, but it's not quite so simple. (And I'm not sure exactly what it is.) -- BenRG 16:11, 26 March 2007 (UTC)

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