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| A '''Malament–Hogarth (M-H) spacetime''', named after [[David B. Malament]] and [[Mark Hogarth]], is a [[theory of relativity|relativistic]] [[spacetime]] that possesses the following property: there exists a [[worldline]] <math>\lambda</math> and an event <math>p</math> such that all events along <math>\lambda</math> are a finite interval in the past of <math>p</math>, but the [[proper time]] along <math>\lambda</math> is infinite. The event <math>p</math> is known as an M-H event. The significance of M-H spacetimes is that they allow for the implementation of certain non-Turing computable tasks ([[hypercomputation]]). The idea is for an observer at some event in <math>p</math>'s past to set a computer (Turing machine) to work on some task and then have the [[Turing machine]] travel on <math>\lambda</math>, computing for all eternity. Since <math>\lambda</math> lies in <math>p</math>'s past, the Turing machine can signal (a solution) to <math>p</math> at any stage of this never-ending task. Meanwhile, the observer takes a quick trip (finite proper time) through spacetime to <math>p</math>, to pick up the solution. The set-up can be used to decide the [[halting problem]], which is known to be undecidable by an ordinary Turing machine. All the observer needs to do is to prime the Turing machine to signal to <math>p</math> if and only if the Turing machine halts.
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| The [[Kerr metric]], which describes empty spacetime around a rotating [[black hole]], possesses these features: a computer can orbit the black hole indefinitely, while an observer falling into the black hole experiences an M-H event as they cross the inner [[event horizon]]. (This, however, neglects the effects of [[Black_hole#Evaporation|Black Hole Evaporation]].) <ref>Etesi, G., and Nemeti, I., 2002 'Non-Turing computations via Malament-Hogarth space-times', Int.J.Theor.Phys. 41 (2002) 341–370, [http://lanl.arxiv.org/abs/gr-qc/0104023 Non-Turing Computations via Malament-Hogarth Space-Times:]</ref>
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| == References==
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| <references/>
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| * Earman, J., 1995, Bangs Crunches Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford: Oxford University Press.
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| * Earman, J. and Norton, J., 1993, ‘Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes’, Philosophy of Science, 5, 22–42.
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| * Earman, J. and Norton, J., 1994, ‘Infinite Pains: The Trouble with Supertasks’, to appear in S. Stich (ed), Paul Benacerraf: The Philosopher and His Critics. New York: Blackwell.
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| * Hogarth, M., 1992, ‘Does General Relativity Allow an Observer to View an Eternity in a Finite Time?’, Foundations of Physics Letters, 5, 173–181.
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| * Hogarth, M., 1994, ‘Non-Turing Computers and Non-Turing Computability’, in D. Hull, M. Forbes, and R. M. Burian (eds), PSA 1994, Vol. 1. East Lansing: Philosophy of Science Association, 126–138. [http://www.hypercomputation.net/resources.html]
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| * Hogarth, M., 1996, 'Computability, Predicability and Spacetime', Ph.D. Thesis, University of Cambridge [http://www.hypercomputation.net/resources.html].
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| * Hogarth, M. 2004, ‘Deciding Arithmetic Using SAD Computers’, The British Journal for the Philosophy of Science 55: 681–691.[http://www.hypercomputation.net/resources.html]
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| * Welch, P.D., 2006, 'The Extent of Computation in Malament-Hogarth Spacetimes', preprint.[http://arxiv.org/abs/gr-qc/0609035]
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| * Manchak, John Byron (2009) On the Possibility of Supertasks in General Relativity. [Preprint] [http://philsci-archive.pitt.edu/id/eprint/5020/]
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| {{DEFAULTSORT:Malament-Hogarth spacetime}}
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| [[Category:General relativity]]
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| [[Category:Hypercomputation]]
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