Kolmogorov-Sinai entropy and black holes

Abstract

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.