I was thinking about black holes, and I know that they form by the death of massive stars. I was wondering, though, do they technically have an "age" when they're born? Do they begin at 0 years at their birth and age over time, kinda like humans? Thanks.
It depends on the context, since "age" is not a trivial concept for nonliving entities. If you're interested in the connections between stellar evolution and black hole evolution, then you might consider the black hole as the last stage of development in a (high mass) star's life. Or if you're considering black holes forming in dense stellar clusters then you might not be very interested in the evolution of the stars themselves (to a point), so the black holes "begin at 0 years" as you say.
In classical general relativity, black holes are solutions to the Einstein field equations (EDIT: parameterized by mass, spin angular momentum and electric charge and maybe more) and they are eternal unless they merge with other black holes. Beyond classical general relativity, i.e. modified gravity, there are other, more exotic possibilities.
Hawking radiation, the prediction of a semi-classical approximation of quantum mechanical effects near an event horizon (it's complicated!), although hypothetical implies black holes "age" on a very long timescale, due to very slowly leaking energy, or "evaporating". The existence of black holes and whether they "age" is an open question in models of quantum gravity.
Lastly, supermassive black holes exist in galactic centers (i.e., not the result of stellar evolution), and it is possible that some have existed as long as galaxies.
One of the results about black holes in classical General Relativity is the "No Hair Theorem". This says that black holes have exactly 3 properties:
- Angular momentum
- Electric charge
All other properties of the matter that falls into a black hole is lost.
Now black holes can change these properties. As matter falls into the black hole, its mass increases. And if that matter is charged then the charge of the black hole can change. Moreover, Hawking radiation can cause the mass of a black hole to decrease, and a rotating black hole can transfer angular momentum to objects as they pass by. So black holes can change with time.
But "age" is not a property of a black hole. A very old black hole with a given mass/angular momentum/charge is identical to a young black hole with the same mass/angular momentum/charge.