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NonTuring computations via MalamentHogarth spacetimes
 Int. J. Theoretical Phys
, 2002
"... We investigate the Church–Kalmár–Kreisel–Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turingtype Theses (not only ..."
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Cited by 79 (8 self)
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We investigate the Church–Kalmár–Kreisel–Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turingtype Theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory, then the above mentioned limitations (predicted by these Theses) become no more necessary, hence certain forms of the Church– Turing Thesis cease to be valid (in general relativity). (For other choices of the background theory the answer might be different.) We also look at various “obstacles ” to computing a nonrecursive function (by relying on relativistic phenomena) published in the literature and show that they can be avoided (by improving the “design ” of our future computer). We also ask ourselves, how all this reflects on the arithmetical hierarchy and the analytical hierarchy of uncomputable functions.
the black hole equilibrium problem been solved
 in Proc. of the 8th Marcel Grossmann Meeting on Relativistic Astrophysics  MG 8
, 1997
"... Abstract. When the term “black hole ” was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the “classical phase ” from 1968 to 1975, and some gaps in the argument h ..."
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Cited by 22 (2 self)
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Abstract. When the term “black hole ” was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the “classical phase ” from 1968 to 1975, and some gaps in the argument have been closed during more recent years. However the presently available demonstration is still subject to undesirably restrictive assumptions such as nondegeneracy of the horizon, as well as analyticity and causality in the exterior. 1
Black hole uniqueness theorems
 In: Proceedings of the 11th International Conference on General Relativity and Gravitation
, 1987
"... I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80’. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black hol ..."
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Cited by 4 (0 self)
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I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80’. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black holes. Its original version was written only few years after my proof of the KerrNewman et al. black hole uniqueness theorem 23 has appeared in print. The proof of the black hole uniqueness theorem relies heavily on the positivity properties of nonlinear sigma models on the Riemannian noncompact symmetric spaces with negative sectional curvature. It is hoped that the first hand description of the original developments leading to our current understanding of the black hole uniqueness will be found useful to all interested in the subject.
Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality
, 706
"... Preprint typeset in JHEP style PAPER VERSION yymm.nnnn LPTHE07 ..."
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Brandon Carter,
, 2006
"... Half century of blackhole theory: from physicists ’ purgatory to mathematicians’ paradise. ..."
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Half century of blackhole theory: from physicists ’ purgatory to mathematicians’ paradise.