Abstract
The so-called Black Hole model of computation involves a non Euclidean space-time where one device is infinitely “accelerated” on one world-line but can send some limited information to an observer working at “normal pace”. The key stone is that after a finite duration, the observer has received the information or knows that no information was ever sent by the device which had an infinite time to complete its computation. This allows to decide semi-decidable problems and clearly falls out of classical computability. A setting in a continuous Euclidean space-time that mimics this is presented. Not only is Zeno effect possible but it is used to unleash the black hole power. Both discrete (classical) computation and analog computation (in the understanding of Blum, Shub and Smale) are considered. Moreover, using nested singularities (which are built), it is shown how to decide higher levels of the corresponding arithmetical hierarchies.
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Throughout the article location is to be understood as a position in space and time and position as only spatial.
This is why we do not talk about any analytic hierarchy.
For example think about the so-called blue-shift effect and how it might be countered (Németi and Dávid 2006, Sub. 5.3.1).
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Disclaimer The author is a computer scientist and not a physicist. So that it is refereed to other contributions in this issue and to the cited bibliography for enlightenment on black holes. The present article aims at providing a context of computation exhibiting the same computing capabilities as black holes and at illustrating the point of view of a computer scientist.
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Durand-Lose, J. Abstract geometrical computation 3: black holes for classical and analog computing. Nat Comput 8, 455–472 (2009). https://doi.org/10.1007/s11047-009-9117-0
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DOI: https://doi.org/10.1007/s11047-009-9117-0