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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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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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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 ..."
Abstract Relativistic computers and the Turing barrier q
"... We examine the current status of the physical version of the ChurchTuring Thesis (PhCT for short) in view of latest developments in spacetime theory. This also amounts to investigating the status of hypercomputation in view of latest results on spacetime. We agree with [D. Deutsch, A. Ekert, R. Lup ..."
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We examine the current status of the physical version of the ChurchTuring Thesis (PhCT for short) in view of latest developments in spacetime theory. This also amounts to investigating the status of hypercomputation in view of latest results on spacetime. We agree with [D. Deutsch, A. Ekert, R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic 6 (3) (2000) 265–283] that PhCT is not only a conjecture of mathematics but rather a conjecture of a combination of theoretical physics, mathematics and, in some sense, cosmology. Since the idea of computability is intimately connected with the nature of time, relevance of spacetime theory seems to be unquestionable. We will see that recent developments in spacetime theory show that temporal developments may exhibit features that traditionally seemed impossible or absurd. We will see that recent results point in the direction that the possibility of artificial systems computing nonTuring computable functions may be consistent with spacetime theory. All these trigger new open questions and new research directions for spacetime theory, cosmology, and computability. Ó 2005 Elsevier Inc. All rights reserved. Of all the entities I have encountered in my life in physics, none approaches the black hole in fascination. And none, I think, is a more important constituent of this universe we call home. The black hole epitomizes the revolution wrought by general relativity. It pushes to an extreme—and therefore tests to the limit—the features of general relativity (the dynamics of curved spacetime) that set it apart from special relativity (the physics of static, ‘‘flat’ ’ spacetime) and the earlier mechanics of Newton. Spacetime curvature. Geometry as part of physics. Gravitational radiation. All of these things become, with black holes, not tiny corrections to older physics, but the essence of newer physics.
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.
Preprint typeset in JHEP style HYPER VERSION Group Averaging for de Sitter free fields
, 810
"... Abstract: Perturbative gravity about global de Sitter space is subject to linearizationstability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant unde ..."
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Abstract: Perturbative gravity about global de Sitter space is subject to linearizationstability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitterinvariant states except the vacuum, though a new Hilbert space of de Sitter invariant states can be constructed via socalled groupaveraging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general Nparticle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.
J H E P10(2014)040
, 2014
"... Charged black holes in stringinspired gravity. I. Causal structures and responses of the BransDicke field Jakob Hansena and Donghan Yeomb,c aKISTI, ..."
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Charged black holes in stringinspired gravity. I. Causal structures and responses of the BransDicke field Jakob Hansena and Donghan Yeomb,c aKISTI,