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27
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.
Static domain walls
 in N = 1 supergravity, Nucl. Phys. B 381
, 1992
"... 1.1 Classes of domain walls....................... 5 1.2 Walls in N = 1 supergravity..................... 6 2 Supergravity theory 9 ..."
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Cited by 39 (6 self)
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1.1 Classes of domain walls....................... 5 1.2 Walls in N = 1 supergravity..................... 6 2 Supergravity theory 9
Theorems on existence and global dynamics for the Einstein equations
 Living Rev. Relativ
"... This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symme ..."
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Cited by 22 (3 self)
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This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity which offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section. 1 1
Conformal Einstein evolution
, 2008
"... We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of spacetimes. ..."
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Cited by 12 (1 self)
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We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of spacetimes.
Inside charged black holes II. Baryons plus dark matter
, 2004
"... This is the second of two companion papers on the interior structure of selfsimilar accreting charged black holes. In the first paper, the black hole was allowed to accrete only a single fluid of charged baryons. In this second paper, the black hole is allowed to accrete in addition a neutral fluid ..."
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Cited by 6 (5 self)
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This is the second of two companion papers on the interior structure of selfsimilar accreting charged black holes. In the first paper, the black hole was allowed to accrete only a single fluid of charged baryons. In this second paper, the black hole is allowed to accrete in addition a neutral fluid of almost noninteracting dark matter. Relativistic streaming between outgoing baryons and ingoing dark matter leads to mass inflation near the inner horizon. When enough dark matter has been accreted that the center of mass frame near the inner horizon is ingoing, then mass inflation ceases and the fluid collapses to a central singularity. A null singularity does not form on the Cauchy horizon. Although the simultaneous presence of ingoing and outgoing fluids near the inner horizon is essential to mass inflation, reducing one or other of the ingoing dark matter or outgoing baryonic streams to a trace relative to the other stream makes mass inflation more extreme, not the other way round as one might naively have expected. Consequently, if the dark matter has a finite crosssection for being absorbed into the baryonic fluid, then the reduction of the amount of ingoing dark matter merely makes inflation more extreme, the interior mass exponentiating more rapidly and to a larger value before mass inflation ceases. However, if the dark matter absorption crosssection is effectively infinite at high collision energy, so that the ingoing dark matter stream
The nature of spacetime singularities
 In 100 Years of Relativity – SpaceTime Structure: Einstein and
, 2005
"... Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are discussed. It is shown how insights on cosmic censorship als ..."
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Cited by 3 (0 self)
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Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are discussed. It is shown how insights on cosmic censorship also arise in connection with the idea of weak null singularities inside black holes. Other topics covered include matter singularities and critical collapse. Remarks are made on possible future directions in research on spacetime singularities. 1
NonAbelian black holes: The inside story
, 1997
"... Recent progress in understanding of the internal structure of nonAbelian black holes is discussed. ..."
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Cited by 2 (1 self)
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Recent progress in understanding of the internal structure of nonAbelian black holes is discussed.
Locality inside black holes violates the second law of thermodynamics
, 2009
"... We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the BekensteinHawking entropy by a large factor. Since only the BekensteinHawking entropy is released during evaporation, the black hole appears to destroy entropy. To avoid this startling resul ..."
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Cited by 1 (0 self)
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We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the BekensteinHawking entropy by a large factor. Since only the BekensteinHawking entropy is released during evaporation, the black hole appears to destroy entropy. To avoid this startling result, the interior of the black hole must contain a proliferation of complementary causal patches — spatially separated regions that are complementary descriptions of the same degrees of freedom. No single observer sees a violation of the second law, and Bousso’s covariant entropy bound, which does not add entropy between different causal patches, is respected. PACS numbers: 04.20.q The entropy calculation presented here was undertaken with a purely astrophysical motivation — to determine how much entropy might be created by Ohmic dissipation inside a highly simplified but plausibly realistic model of a supermassive black hole. We had no intention of probing locality, entropy bounds, complementarity, or any of the other esoteric features of black holes that have exercised quantum gravity enthusiasts and string theorists since the discovery of Hawking radiation [1, 4, 8, 11, 14, 15]. However, the calculation’s alarming result, an entropy many orders of magnitude greater than the BekensteinHawking entropy, forced us to confront these issues, and in the process provided new evidence for prolific complementarity inside black holes. The reader who is willing to accept the black hole model is invited to go directly to the Discussion section.
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
Inside charged black holes I. Baryons
, 2008
"... An extensive investigation is made of the interior structure of selfsimilar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated self ..."
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Cited by 1 (1 self)
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An extensive investigation is made of the interior structure of selfsimilar accreting charged black holes. In this, the first of two papers, the black hole is assumed to accrete a charged, electrically conducting, relativistic baryonic fluid. The mass and charge of the black hole are generated selfconsistently by the accreted material. The accreted baryonic fluid undergoes one of two possible fates: either it plunges directly to the spacelike singularity at zero radius, or else it drops through the Cauchy horizon. The baryons fall directly to the singularity if the conductivity either exceeds a certain continuum threshold κ∞, or else equals one of an infinite spectrum κn of discrete values. Between the discrete values κn, the solution is characterized by the number of times that the baryonic fluid cycles between ingoing and outgoing. If the conductivity is at the continuum threshold κ∞, then the solution cycles repeatedly between ingoing and outgoing, displaying a discrete selfsimilarity reminiscent of that observed in critical collapse. Below the continuum threshold κ∞, and except at the discrete values κn, the baryonic fluid drops through the Cauchy horizon, and in this case undergoes a shock, downstream of which the solution terminates at an irregular sonic point where the proper acceleration diverges, and there is no consistent selfsimilar continuation to zero radius. As far as the solution can be followed inside the Cauchy horizon, the radial direction is timelike. If the radial direction remains timelike to zero radius (which cannot be confirmed because the selfsimilar solutions terminate), then there is presumably a spacelike singularity at zero radius inside the Cauchy horizon, which is distinctly different from the vacuum (ReissnerNordström) solution for a charged black hole. PACS numbers: 04.20.q I.