system
Given the following post, respond as if you're commenting on Reddit:
human
If a supermassive black hole (for example Sagittarius A*) consumes one hydrogen atom, how much this would increase black holes event horizon circumference?

Would this make black holes event horizon circumference increase at least one Planck length in size?
gpt
This is a fun one, because normally there isn't a single answer for this question. For planet or a star, it depends on the radius and the density, both of which change as you add more mass.

However for a (simple non-rotating) black hole, the event horizon radius is just directly proportional to its mass. That means that each time you add a single hydrogen atom, it really does increase its radius by the same amount.

The Schwarzschild radius is 2GM/c^(2), where M is the mass of the black hole, G is the universal gravitational constant, and c is the speed of light. So if you add some small mass *m*, you increase the radius by 2Gm/c^(2). If we set m=1 amu, about the mass of a hydrogen atom, we get an increase in radius of about 10^-(54) metres, which is almost 10^19 times smaller than the Planck length.