Black holes for financiers

No, that's not a typo: it's black holes, not Black Scholes :-) I posted the following comment on Brad Setser's blog (mostly read by finance and econ types). He was fascinated by this Times article on a measurement of the size of the supermassive black hole at the center of our galaxy.

It's now widely believed that many galaxies have at their centers supermassive black holes with masses larger than a million solar masses. (The existence of these supermassive holes is a plausible consequence of how galaxies are formed through non-linear growth of density perturbations in the early universe, but that is another story.) Because black holes are dense, even these supermassive black holes are not that large. The one at the center of our galaxy appears to have diameter roughly that of the earth-sun distance (= 93 million miles; the galaxy is 10^9 times larger), and a mass of 4 million solar masses.

It is easy for astronomers to find objects which are so dense that, theoretically, they must be black holes. The thing at the center of our galaxy is one example; there are many more that are remnants of stellar evolution (very large stars that run out of fuel and collapse to form black holes -- these are only a few orders of magnitude more massive than our sun). To estimate the density astronomers need to measure the mass (based on the gravitational pull exerted on nearby objects such as stars) and size of the object.

The recently reported findings have to do with radio astronomers looking at the black spot caused by absorption of radio waves coming from behind the black hole. They can measure the radius of the black spot to estimate the size of the black hole.

What is most interesting about black holes is the general relativistic effects associated with their "horizon" -- particles, even photons, which pass the horizon can never escape and are doomed to eventually fall into the "singularity" inside the black hole where (according to general relativity) known physics must break down. Unfortunately, based on what I just said, outside observers will never know what happens at the singularity since the object falling in cannot send a signal back out once it has passed the horizon!

To establish the properties of the horizon predicted by general relativity would require probes which signal back to us as they fall in. (They would go dark just as they hit the horizon -- their signal would be "infinitely redshifted.") Astronomical observations are not really enough (although these radio observations are a step in the right direction) since in principle a very dense object which isn't necessarily a black hole might absorb photons (radio waves) to yield a black spot. The identification of an object as a black hole simply based on its density relies on general relativity in a domain in which the theory has not been tested experimentally.