system
Given the following post, respond as if you're commenting on Reddit:
human
Does the mass of a black hole increase by any appreciable amount by absorbing photons?

We all know that light cannot escape from black holes. Over the course of tens/hundreds/thousands of millions of years, does a black hole absorb so much light that its mass could measurably increase?
gpt
The mass of the black hole will increase by exactly the energy of the light absorbed, divided by c^(2). This is just conservation of energy combined with E=mc^(2) for the black hole.

I did a very VERY rough estimate for the total mass gained by the supermassive black hole at the center of the Milky Way (Sag A*). The combined luminosity of all ~100 billion stars, from ~10 kiloparsecs away on average, shining for 10 billion years, increases the mass of the black hole by one quadrillionth (10^(-15)) of the mass of the Sun. (That's still a quadrillion kilograms, but it's tiny compared to an astrophysically measurable amount of mass.)

Basically, even though the black hole absorbs all the light that hits it, it's so compact that most of the light misses it.