On black hole thermodynamics, singularity, and gravitational entropy

Why is black hole entropy affected by rotation?

“…Here r H is the radial coordinate at the event horizon, and ℓ 4 is the four-dimensional Planck length. (The extremal case is Q 2 = 4πℓ 2 4 M 2 , so indeed, as claimed above, the (specific) entropy in that case is one quarter of the corresponding Schwarzschild specific entropy, 4πMℓ 2 4 .) It is obvious in this case that the specific entropy is indeed a monotonically decreasing function of the charge, assuming the mass to be fixed.…”

“…The celebrated Kerr black hole in the Cygnus X-1 system has many interesting properties. One of the less-discussed of these properties is that the specific entropy (that is, the entropy [1,2] per unit mass) of this black hole has only slightly more than half of the value it would have if it were a Schwarzschild black hole of the same mass. This can be deduced from the formula for the specific entropy of a Kerr black hole (see below) and from the fact that the angular momentum of the Cygnus X-1 black hole is close to the maximum value permitted by Cosmic Censorship: the angular momentum per mass squared (in Planck units), a * , which is unity for an exactly extremal Kerr black hole, is claimed in [3] to be at least 1 0.9696 for Cygnus X-1.…”

“…What is mysterious is that rotation should be in any way related to the black hole entropy. 2 It is true that the "rotation" of a black hole is actually a rather subtle matter; a black hole is not a physical object, so it does not "rotate" in the usual sense. Even leaving this to one side, a black hole does not rotate as if it were a rigid body -for example, when the two horizons are distinct they have different angular velocities [10].…”

“…The gauge-gravity duality [18][19][20][21][22] offers the possibility of approaching black hole entropy through a study of conformal field theories and related strongly coupled field theories. This approach has enjoyed several notable recent successes [23][24][25] in computing black hole 2 We note in passing that this phenomenon plays an important role in applications of the Second Law of thermodynamics to black hole fragmentation [8] (because the fact that extremal black holes have the smallest possible entropy among black holes of a given mass allows one to put a lower bound on the entropy of the fragments), and it is fundamental in studies of the Penrose bound [9]. 3 For example, one can ask this question in the context of the recent remarkable work of Balasubramanian et al [11].…”

“…Some holographic formulations of the problem of identifying black hole microstates emphasise the possibility that the latter might perhaps be not very different from the microstates of other forms of strongly coupled matter. The concept of "black hole molecules" [27] belongs to this category; see also more recent work along these lines summarised in [2,28].…”