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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 66 (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.
Perturbation theory of spherically symmetric selfsimilar black holes
, 706
"... The theory of perturbations of spherically symmetric selfsimilar black holes is presented, in the NewmanPenrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is giv ..."
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Cited by 1 (0 self)
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The theory of perturbations of spherically symmetric selfsimilar black holes is presented, in the NewmanPenrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is given. Monopole and dipole modes are treated. The NewmanPenrose wave equations governing polar and axial spin0 perturbations are explored. PACS numbers: 04.20.q
The interior structure of slowly rotating black holes
, 903
"... Abstract. The internal structure of a slowly rotating, charged black hole that is undergoing mass inflation at its inner horizon is derived. The equations governing the angular behavior decouple from the radial behavior, so all conclusions regarding inflation in a spherical charged black hole carry ..."
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Abstract. The internal structure of a slowly rotating, charged black hole that is undergoing mass inflation at its inner horizon is derived. The equations governing the angular behavior decouple from the radial behavior, so all conclusions regarding inflation in a spherical charged black hole carry through unchanged for a slowlyrotating black hole. Quantities inflate only in the radial direction, not in the angular direction. Exact selfsimilar solutions are obtained. For sufficiently small accretion rates, the instantaneous angular motion of the accretion flow has negligible effect on the angular spacetime structure of the black hole, even if the instantaneous angular momentum of the accretion flow is large and arbitrarily oriented. PACS numbers: 04.20.qThe interior structure of slowly rotating black holes 2 1.
The physics of the relativistic counterstreaming instability
, 811
"... that drives mass inflation inside black holes ..."
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.