Schwarzschild radius

It is given by 2 M G / c², so if you have a black hole of radius r, its mass is M = r c² / 2 G. A black hole of radius 1 m is about 100 Earth masses. The temperature is inversely proportional to the mass and a one-gram black hole has a temperature of 10²⁶ kelvins. It evaporates by Hawking radiation in 10^-27 second.

G is of course the gravitational constant.

This is interesting because the volume increases as the cube of the radius (double the radius is eight times the volume). This means that as the mass is proportional to the radius (from the equation) the required density for the matter is lowered as the amount of matter rises.

I seem to remember a discussion a few years ago that once you got up to the scale of the known universe then the theoretical Schwarzschild radius was actually larger than the universe. Does this mean that we live inside an enourmous black hole?

The answer I suspect is that we don't have nearly enough knowledge about the universe and attempting to apply a rule for one situation to a more general situation is fraught with danger. Like applying Newtonian physics to relativistic situations.

It does however lead to all sorts of interesting speculation about black holes within black holes and such.

Not being a physicist this is the limit of my knowledge but I'm sure there is someone out there who can expand on (and maybe replace) this node.

It should be noted that the Schwarzschild radius only applies to spherical objects, and is a consequence of his description of the space-time geometry around any spherical object, not necessarly a black hole. Published in 1915, (soon after Einsteins general theory of relativity), it makes the remarkable prediction, if you take any spherical mass and compress it, when its size hits the Schwarzschild radius the gravity will be so strong; the space-time so bent, not even light can escape. The 'surface' this radius describes is more commonly called the event horizion, as you cannot see past it; the light of your torch would disappear, no reflections would return to carry information to your eyes.

This radius can be as small or as big as you like, you simply have to have enough mass within it; and so you can have black holes smaller than the size of an atomic nucleus, through to the size of the solar system, or even bigger... Interestingly, if you churn through the equations, looking at how the density of the object changes with radius, you find the density goes down as the radius goes up. So by the time you get to a supermassive black hole the size of a solar system, its density is comparable to water...

In pursuit of generality; trying to find out what happens to massive irregulary shaped objects, Kip Thorne formulated the hoop conjecture. In this there is a critical circumference of the mass in question which determines whether or not collapse to a black hole is inevitable. if the object can be passed through the a hoop with this circumference, it will collapse to a black hole.

Just an etymological note: the name 'Schwarzschild' breaks down in German as black (schwarz) shield (schild), which is astonishingly appropriate for the notion of a Schwarzschild radius, considering it is actually named after the scientist, Karl Schwarzschild, who first calculated it, in 1916.