arXiv subjects
Publications and source records attributed to Kostiantyn Ropotenko.
It is shown that the fast scrambling of information in a black hole can be viewed as Brownian motion of information in a fluid with negative viscosity (and negative temperature). It is argued that a non-local character of the fast scrambling is only an illusion; the stretched horizon with negative viscosity is an amplifying medium that mimics non-locality and superluminal communication.
A diffusion equation for a black hole is derived from the Bunster-Carlip equations. Its solution has the standard form of a Gaussian distribution. The second moment of the distribution determines the quantum of black hole area. The entropy of diffusion process is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy.
It is believed that the first law of black-hole mechanics has no independent physical significance and acquires it only after identifying with the first law of thermodynamics. It is argued here that the first law of black-hole mechanics has a direct physical significance: not only the term $ΩdJ$ but all its terms have the same mechanical meaning - the rotational kinetic energy of a black hole in real or in an internal space. Moreover, it is shown that the Kerr-Newman black hole is a system of non-degenerate plane rotators represented by the corresponding terms in the first law of black-hole mechanics. It is found that a degeneracy arises because the energy of a black hole does not depend on where an internal angular momentum of a black hole associated with the black hole area is determined on the horizon.
In contrast to alternative values, the quantum of area $ΔA = 8πl_P^{2}$ does not follow from the usual statistical interpretation of black hole entropy; on the contrary, a statistical interpretation follows from it. This interpretation is based on the two concepts: nonadditivity of black hole entropy and Landau quantization. Using nonadditivity a microcanonical distribution for a black hole is found and it is shown that the statistical weight of black hole should be proportional to its area. By analogy with conventional Landau quantization, it is shown that quantization of black hole is nothing but the Landau quantization. The Landau levels of black hole and their degeneracy are found. The degree of degeneracy is equal to the number of ways to distribute a patch of area $8πl_P^{2}$ over the horizon. Taking into account these results, it is argued that the black hole entropy should be of the form $S_{bh} =2π\cdotΔΓ$, where the number of microstates is $ΔΓ= A/8πl_P^{2}$. The nature of the degrees of freedom responsible for black hole entropy is elucidated. The applications of the new interpretation are presented. The effect of noncommuting coordinates is discussed.