Kolmogorov-Sinai and Bekenstein-Hawking entropies

Abstract

It is shown that instability of stringy matter near the event horizon of a black hole (the spreading effect) can be characterized by the Lyapunov exponents. The Kolmogorov-Sinai entropy is the sum of all the positive Lyapunov exponents and equals to the inverse gravitational radius. Due to a replacement of the configuration space of a string by its phase space at distance of order of the string scale, the relation between the Kolmogorov-Sinai and Bekenstein-Hawking entropies is established. The KS entropy of a black hole measures the rate at which information about the state of a string collapsing into the black hole is lost with time as it spreads over the horizon.