Black hole as a model of computation

Abstract

This paper focuses on an alternative, more physically realistic model of computation than Etesi and Németi’s relativistic computer in a Malament-Hogarth spacetime (2002) that uses the black hole itself combined with an external observer equipped with a source and some method of measurement of gamma-rays, as opposed to sending a classical computer into a black hole and exploiting the properties of the spacetime to achieve hypercomputation. The source of output, Hawking radiation, is considered along with the constraints imposed by the holographic principle which limit the number of degrees of freedom in the system and consequently the maximum usable information. The Bekenstein-Hawking entropy is converted from the traditional form in terms of the horizon area to that of the Shannon entropy, establishing an analogy between the physical and computational perspectives of the system. Next examples are considered to establish the approximate order of the necessary excitation energy and the resulting gamma-ray interactions which form the input from the observer. Finally, the Turing completeness of the language for this model is considered through a simulation of the Turing machine. The goal is to introduce a model of computation that can later be used to study the relationship between computability and physical systems. Keywords: Black hole computation, Kerr/CFT correspondence, Holographic principle, Information theory, Gamma-ray spectroscopy, Shannon entropy