Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: benm on 12/04/2019 10:10:10

Michael is in the dark about this one:
I understand we can measure the circumference of a black holes event horizon, but as the singularity bends space, can we accurately measure the diameter? Does the hole's circumference and diameter bear the same ration as other physical 'spheres'?
Can anybody help shine some light on it?

To answer the second question first, space is bent anywhere around an object with mass, so the space is not Euclidean around them. You can take a measuring stick and count off the meters of say Earth's circumference and get its proper distance. You can then divide that value by 2π and compute the Earth's Schwarzschild radial distance, which will be a bit less than the proper radius you would similarly measure with the stick.
The difference between the two is more and more the more dense the object. With a black hole, the proper distance cannot be measured since there is no way to do it with a stick and the computed value is meaningless.
So to answer the first question, the circumference of the black hole is a limit of the proper circumference as the radius approaches the event horizon. You can't actually do it directly at the event horizon since there is no way to put a measuring stick there. The Schwarzschild diameter is just that circumference /π, and that is the only meaningful value we have to work with. There is no diameter more real than that. Mathematically, there is an infinite or undefined 'distance' to the center (computed different ways). It isn't a proper distance since there is no way to orient the stick along the line we wish to measure. It isn't really spatial distance inside the event horizon.