Title: Black-Hole Entropy: its Key Role in the 2nd Law of Thermodynamics
Abstract: Observational cosmology reveals the presence, in the current universe, of supermassive black holes whose total entropy should easily dominate that of the entire universe, according to the fundamental Bekenstein-Hawking formula. But this was not always the case. At the time of the emission of the microwave background radiation, some 380,000 years following the Big Bang, the entropy contribution from gravitational effects was extremely tiny, that in the matter having been extremely close to the maximum that it could have been. For some reason, at the Big bang itself, gravitational degrees of freedom were enormously suppressed, thereby allowing the 2nd Law of Thermodynamics to operate, as gravitational degrees relentlessly became activated, leading to their domination in the black holes currently observed.
But what about the remote future? We must expect that this trend will continue, even to the final evaporation of the black holes in an ever exponentially expanding universe. A seeming paradox lies behind this picture, in the extreme difference between the singularity structure at the Big Bang, where gravitational degrees of freedom are strangely suppressed, and the very opposite in the singularities in black holes, whose singularities appear to have the maximum entropy possible. It is hard to see how any direct quantization of gravity can resolve this gross time-asymmetric puzzle. Indeed, it can be argued that any quantization of gravity cannot resolve this issue without, apparently, an accompanying “gravitization” of quantum theory, in which the fundamental “measurement problem” of quantum mechanics is also resolved. Such a theory is currently lacking, but various experiments are now under serious consideration, to test this very basic idea.
Nevertheless, a deeper understanding of the special nature of the Big Bang can be illuminated by examining it from the perspective of conformal geometry, according to which the Big-Bang singularity becomes non-singular, this being quite different from the situation arising from the singularities in black holes. In conformal geometry, big and small become equivalent, which can only hold for a singularity of the type we seem to find at the Big Bang. This situation is also relevant in relating the extremely hot and dense Big Bang to the extremely cold and rarefied remote future of a previous “cosmic aeon”, leading to the picture of conformal cyclic cosmology (CCC) according to which our Big Bang is viewed as the conformally continued remote future of a previous cosmic aeon. It turns out that there are now certain strong observational signals, providing some remarkable support for this highly non-intuitive but mathematically consistent CCC picture.