### A comment about thermodynamics of dark black holes

Lubos Motl had an excellent posting about thermodynamics of black holes. Unfortunately I am too busy with the updatings for a detailed response. Just a hasty comment about thermodynamics of dark black holes inspired by the vision about dark matter as a hierarchy of phases with non-standard value of Planck constant realized in terms of a book like structure of the generalized imbedding space (generalization of H=M

^{4}×CP

_{2}) with pages labeled by the values of Planck constant and phase transitions changing Planck constant interpreted as a leakage between different pages of the Big Book.

Suppose we accept the identification of dark matter in astrophysical length scales as matter with a gigantic gravitational Planck constant suggested by Bohr orbitology of planetary orbits. For instance, hbar =GM^{2}/v_{0}, v_{0}=1/4, would hold true for an ideal black hole with Planck length (hbarG)^{1/2} equal to Schwartshild radius 2GM. Since black hole entropy is inversely proportional to hbar, this would predict black hole entropy to be of order single bit. This of course looks totally non-sensible if one believes in standard thermodynamics. For the star with mass equal to 10^{40} Planck masses discussed in the example of Lubos the entropy associated with the initial state of the star would be roughly the number of atoms in star equal to about 10^{60}. Black hole entropy proportional to GM^{2}/hbar would be of order 10^{80} provided the standard value of hbar is used as unit.

This stimulates some questions.

- Does second law pose an upper bound on the value of hbar of dark black hole from the requirement that black hole has at least the entropy of the initial state. The maximum value of hbar would be given by the ratio of black hole entropy to the entropy of the initial state and about 10
^{20}in the example of Lubos to be compared with GM^{2}/v_{0}≈10^{80}. - Or should one generalize thermodynamics in a manner suggested by zero energy ontology by making explicit distinction between subjective time (sequence of quantum jumps) and geometric time? The arrow of geometric time would correlate with that of subjective time. One can argue that the geometric time has opposite direction for the positive and negative energy parts of the zero energy state interpreted in standard ontology as initial and final states of quantum event. If second law would hold true with respect to subjective time, the formation of ideal dark black hole would destroy entropy only from the point of view of observer with standard arrow of geometric time. The behavior of phase conjugate laser light would be a more mundane example. Do self assembly processes serve as example of non-standard arrow of geometric time in biological systems? In fact, zero energy state is geometrically analogous to a big bang followed by big crunch. One can however criticize the basic assumption as ad hoc guess. One should really understand the the arrow of geometric time. This is discussed in detail in the article About the Nature of Time.