Do galaxies have habitable zones the same as stars do? Say in a galaxy with a very active nucleus producing a lot of heat and radiation, would there be a point at which no star's planets could harbor life do to the effects of the black hole? Also would there possibly be a habitable zone for galaxy clusters? If there were many galaxies with extremely active galactic nuclei condensed closely together would this possibly also hinder the evolution of life?
I'll be honest. I looked up Galactic Habitable Zone on Wikipedia. The idea was introduced in 1986 and expanded upon in the book "Rare Earth" by Brownlee and Ward. Essentially the idea is that in the bulge there is too much activity (supernovae, etc.) and in the halo of the galaxy there is not enough heavy elements (carbon, etc.) for life to exist. This was in reference to complex life "as we know it" (Check out another Peter Ward book entitled "Life As We Do Not Know It"). Stellar habitable zones are based on the presence of liquid water. This definition would greatly increase the theoretical "Galactic Habitable Zone". I think we need to look at a region and calculate all of the pluses and minuses of that specific region then keep our minds open.
stars themselves, like our sun does, have a heliosphere. the size of this heliosphere would vary depending on the size/strength of the star and it's position in the galaxy. and what happens outside the heliosphere has usually little effect inside, in terms of radiation. so, the presence of a black hole or an agn near the star doesn't matter as long as the star itself is strong to create a large heliosphere (in which the planets reside). we can talk about the problem case by case but i don't know of a general galactic version of the goldilocks zone.
The zone, you mean, in galaxies would be very unstable - huge changes in electromagnetic flux (something like explosions) because of more dynamic changes of the environment there (than in the outer rim of galaxy: black hole, jets, etc...) - so there is considered lower probability of life in the center of galaxies (or Galaxy). But in fact I think we have to few information about galaxies to seriously think about probability of life on free planets close to the center of the Galaxy (the more other galaxies).