Black hole motion in Euclidean space as a diffusion process

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.Comment: 6 pages, no figures; v.2: a mistake in deriving of the diffusion equation corrected; a relation between the entropy of diffusion process and the Bekenstein-Hawking entropy correcte

What is the maximum rate at which entropy of a string can increase?

According to Susskind, a string falling toward a black hole spreads exponentially over the stretched horizon due to repulsive interactions of the string bits. In this paper such a string is modeled as a self-avoiding walk and the string entropy is found. It is shown that the rate at which information/entropy contained in the string spreads is the maximum rate allowed by quantum theory. The maximum rate at which the black hole entropy can increase when a string falls into a black hole is also discussed.Comment: 11 pages, no figures; formulas (18), (20) are corrected (the quantum constant is added), a point concerning a relation between the Hawking and Hagedorn temperatures is corrected, conclusions unchanged; accepted by Physical Review D for publicatio

Kolmogorov-Sinai entropy and black holes

It is shown that stringy matter near the event horizon of a Schwarzschild black hole exhibits chaotic behavior (the spreading effect) which can be characterized by the Kolmogorov-Sinai entropy. It is found that the Kolmogorov-Sinai entropy of a spreading string equals to the half of the inverse gravitational radius of the black hole. But the KS entropy is the same for all objects collapsing into the black hole. The nature of this universality is that the KS entropy possesses the main property of temperature: it is the same for all bodies in thermal equilibrium with the black hole. The Kolmogorov-Sinai entropy measures the rate at which information about the string is lost as it spreads over the horizon. It is argued that it is the maximum rate allowed by quantum theory. A possible relation between the Kolmogorov-Sinai and Bekenstein-Hawking entropies is discussed.Comment: 10 pages, no figures; this is an extended version of my paper arXiv:0711.313