I am a bit confused about the independent parameters in a charged black hole in AdS spaces. From equation (63) of this lecture notes we see that the temperature (T) of the black hole has chemical potential ($\mu$) dependence.
I was wondering, if one wishes to work in this background (using holography) what are the free parameters one can play with?
What are the basic differences between canonical and grand canonical ensemble description of this system? Also which ensemble should one choose to work with depending on the problem?
- What does $\mu \to 0$ mean? Here it seems like charge-free limit. But this limit appears also in Bose-Einstein condensate. Isn't this a bit subtle?