Can you go to the other side of a black hole? As in, is a black hole a sphere that you can "go to the other side of," or if you orbited it from lightyears away, could you go "around" it?
It is, in fact, possible to orbit a black hole. You do not even have to be light years outside of it. You simply have to be outside the event horizon, the distance at which everything, even light, falls into the black hole. For a normal-sized black hole, between fifty and seventy miles is a safe distance to orbit.
A black hole is a sphere in the sense that everything that goes within its Schwarzschild radius (the distance from the center of the black hole to the event horizon) cannot escape its gravity. Thus, there is a dark sphere around the infinitely dense center, or singularity, from which nothing can escape.
There is a supermassive black hole at the center of the Milky Way, and we orbit this black hole approximately every 230 million years.
Edit by Michael Lam on August 21, 2015: To answer the title question, if a black hole is rotating, then it will be shaped as an oblate spheroid, slightly larger around the equator than in the direction of the poles. However, the equations of general relativity tell us that rather than having one radius, the location of the event horizon, there are two important radii, the spherical event horizon on the inside, and the oblate spheroidal exterior surface. The region in between the two is called the ergosphere, where particles cannot remain at rest and objects can still escape the black hole. Such a black hole looks like this:
As in the non-rotating case, no particle entering the event horizon can escape.
This page was last updated on August 21, 2015.