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21
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 73 (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 42 (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
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 7 (6 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
Charged False Vacuum Bubbles and the AdS/CFT Correspondence
, 1999
"... We initiate a study of cosmology within the framework of Maldacena’s AdS/CFT correspondence. We present a comprehensive analysis of the classical motion of a charged domain wall that separates an external ReissnerNordstrøm region of spacetime (with small or vanishing cosmological constant) from an ..."
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We initiate a study of cosmology within the framework of Maldacena’s AdS/CFT correspondence. We present a comprehensive analysis of the classical motion of a charged domain wall that separates an external ReissnerNordstrøm region of spacetime (with small or vanishing cosmological constant) from an internal deSitter region. The possible associated spacetime diagrams are drawn, although in the classical case, an unambiguous prediction of what occurs at late times in the interior region is not possible, since singularities and Cauchy horizons form. We argue that, when the asymptotic region is antide Sitter, the AdS/CFT correspondence gives a prescription for resolving the curvature singularities and evolving solutions across the expected Cauchy horizon. Some of our solutions contain inflating interiors, and we provide evidence these can be patched onto solutions with smooth initial data, circumventing an obstacle found by Farhi and Guth to creating an inflating universe in the laboratory. BROWNHET1186 CWRUP2299
On thermodynamical properties of some coset cft backgrounds
 JHEP
"... We investigate the thermodynamical features of two Lorentzian signature backgrounds that arise in string theory as exact CFTs and possess more than two disconnected asymptotic regions: the 2d charged black hole and the NappiWitten cosmological model. We find multiple smooth disconnected Euclidean ..."
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We investigate the thermodynamical features of two Lorentzian signature backgrounds that arise in string theory as exact CFTs and possess more than two disconnected asymptotic regions: the 2d charged black hole and the NappiWitten cosmological model. We find multiple smooth disconnected Euclidean versions of the charged black hole background. They are characterized by different temperatures and electrochemical potentials. We show that there is no straightforward analog of the HartleHawking state that would express these thermodynamical features. We also obtain multiple Euclidean versions of the NappiWitten cosmological model and study their singularity structure. It suggests to associate a nonisotropic temperature with this background. 1
hepth/0401209 On the Resolution of the TimeLike Singularities in
, 2004
"... Abstract: Certain timelike singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The ReissnerNordström singularity allows f ..."
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Abstract: Certain timelike singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The ReissnerNordström singularity allows for communication through the singularity and can be termed “beam splitter ” since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is ω −4/3. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negativemass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d> 4.Contents
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.
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
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.
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.