I'm currently reading Carlo Rovelli's Seven Brief Lessons on Physics, and I find it quite fascinating. Of course, the book gives mostly an overview of modern physics without going too much into details or equations and the like, stressing more the journey through physics that we have undertaken in the last century.
However, in the book Rovelli explains that the studies of thermodynamics and statistical mechanics "were extended to electromagnetic and quantum phenomena. Extension to include the gravitational field, however, has proved problematic. How the gravitational field behaves when it heats up is still an unsolved problem." (pgs 57-58) He then describes how heat causes the electromagnetic waves in an electromagnetic field to vibrate, but adds that it is unknown as to how heat affects a gravitational field. Since gravity by Einstein's theory of general relativity is in essence the curvature of space-time, heating a gravitational field would also result in the heating of time. However, as Rovelli states, "what is a vibrating time?" (pg 58)
Later on in the book, however, Rovelli mentions that Stephen Hawking calculated that "black holes are always 'hot.' They emit heat like a stove." (pg 63) From my perspective, couldn't the heat emitted from the black hole affect its gravitational field? From my knowledge, black holes have an enormous gravitational field as to not allow light to escape its grasp, and time in a black hole essentially stops. It seems to me, then, that two things are at work here: the gravitational field of the black hole, and the heat of the black hole. Since heat can, apparently, affect a gravitational field (in a way that is currently unknown), is it possible that time as witnessed near a black hole (where it essentially stops) is a result of the black hole's gravity, of its heat, or both? Could it also add to our understanding of the way heat affects a gravitational field?
Note: my knowledge of black holes is fairly limited, as it is of modern physics, so criticism on my logic is requested as is a refined understanding pertaining to any misconception I may have.