Kolmogorov-Sinai and Bekenstein-Hawking entropies

Details Kolmogorov-Sinai and Bekenstein-Hawking entropies Kolmogorov-Sinai and Bekenstein-Hawking entropies

2007-11-20

arxiv.org/abs/0711.3131v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, no figures; factors in Eqns. (12), (21) corrected; structure of the paper improved; main results and conclusions unch

Scientific paper

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.

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