71,894 research outputs found

    Living on the edge: cosmology on the boundary of anti-de Sitter space

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    We sketch a particularly simple and compelling version of D-brane cosmology. Inspired by the semi-phenomenological Randall--Sundrum models, and their cosmological generalizations, we develop a variant that contains a single (3+1)-dimensional D-brane which is located on the boundary of a single bulk (4+1)-dimensional region. The D-brane boundary is itself to be interpreted as our visible universe, with ordinary matter (planets, stars, galaxies) being trapped on this D-brane by string theory effects. The (4+1)-dimensional bulk is, in its simplest implementation, adS_{4+1}, anti-de Sitter space. We demonstrate that a k=+1 closed FLRW universe is the most natural option, though the scale factor could quite easily be so large as to make it operationally indistinguishable from a k=0 spatially flat universe. (With minor loss of elegance, spatially flat and hyperbolic FLRW cosmologies can also be accommodated.) We demonstrate how this model can be made consistent with standard cosmology, and suggest some possible observational tests.Comment: LaTeX2e, 17 pages; Revised (references added, physics unchanged). To appear in Physics Letters

    Quantum Interest in (3+1) dimensional Minkowski space

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    The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.Comment: V1: 8 pages, revtex4; V2: 10 pages, some technical changes in details of the argument, no change in physics conclusions, this version essentially identical to published versio

    The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction

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    In this note I introduce the notion of the ``reliability horizon'' for semi-classical quantum gravity. This reliability horizon is an attempt to quantify the extent to which we should trust semi-classical quantum gravity, and to get a better handle on just where the Planck regime resides. I point out that the key obstruction to pushing semi-classical quantum gravity into the Planck regime is often the existence of large metric fluctuations, rather than a large back-reaction. There are many situations where the metric fluctuations become large long before the back-reaction is significant. Issues of this type are fundamental to any attempt at proving Hawking's chronology protection conjecture from first principles, since I shall prove that the onset of chronology violation is always hidden behind the reliability horizon.Comment: 6 pages; ReV_TeX 3.0; two-column format. Revisions: Central definitions and results essentially unchanged. Discussion of the relationship between this letter and the Kay-Radzikowski-Wald singularity theorems greatly extended and clarified. Discussion of reliability horizon near curvature singularities modified. Several references added. Minor typos fixed. Technical TeX modification

    The Small-Is-Very-Small Principle

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    The central result of this paper is the small-is-very-small principle for restricted sequential theories. The principle says roughly that whenever the given theory shows that a property has a small witness, i.e. a witness in every definable cut, then it shows that the property has a very small witness: i.e. a witness below a given standard number. We draw various consequences from the central result. For example (in rough formulations): (i) Every restricted, recursively enumerable sequential theory has a finitely axiomatized extension that is conservative w.r.t. formulas of complexity ≤n\leq n. (ii) Every sequential model has, for any nn, an extension that is elementary for formulas of complexity ≤n\leq n, in which the intersection of all definable cuts is the natural numbers. (iii) We have reflection for Σ20\Sigma^0_2-sentences with sufficiently small witness in any consistent restricted theory UU. (iv) Suppose UU is recursively enumerable and sequential. Suppose further that every recursively enumerable and sequential VV that locally inteprets UU, globally interprets UU. Then, UU is mutually globally interpretable with a finitely axiomatized sequential theory. The paper contains some careful groundwork developing partial satisfaction predicates in sequential theories for the complexity measure depth of quantifier alternations

    Tolman mass, generalized surface gravity, and entropy bounds

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    In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and invoking the Unruh effect one can then develop elementary bounds on the quasi-local entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some notational changes for clarity; introductory paragraph rewritten; no physics changes. This version accepted for publication in Physical Review Letter

    Explicit form of the Mann-Marolf surface term in (3+1) dimensions

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    The Mann-Marolf surface term is a specific candidate for the "reference background term" that is to be subtracted from the Gibbons-Hawking surface term in order make the total gravitational action of asymptotically flat spacetimes finite. That is, the total gravitational action is taken to be: (Einstein-Hilbert bulk term) + (Gibbons-Hawking surface term) - (Mann-Marolf surface term). As presented by Mann and Marolf, their surface term is specified implicitly in terms of the Ricci tensor of the boundary. Herein I demonstrate that for the physically interesting case of a (3+1) dimensional bulk spacetime, the Mann-Marolf surface term can be specified explicitly in terms of the Einstein tensor of the (2+1) dimensional boundary.Comment: 4 pages; revtex4; V2: Now 5 pages. Improved discussion of the degenerate case where some eigenvalues of the Einstein tensor are zero. No change in physics conclusions. This version accepted for publication in Physical Review

    Rastall gravity is equivalent to Einstein gravity

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    Rastall gravity, originally developed in 1972, is currently undergoing a significant surge in popularity. Rastall gravity purports to be a modified theory of gravity, with a non-conserved stress-energy tensor, and an unusual non-minimal coupling between matter and geometry, the Rastall stress-energy satisfying nabla_b [T_R]^{ab} = {\lambda/4} g^{ab} nabla_b R. Unfortunately, a deeper look shows that Rastall gravity is completely equivalent to Einstein gravity --- usual general relativity. The gravity sector is completely standard, based as usual on the Einstein tensor, while in the matter sector Rastall's stress-energy tensor corresponds to an artificially isolated part of the physical conserved stress-energy.Comment: V1: 5 pages. V2: 6 pages; 5 added references, some added discussion, no changes in physics conclusions. V3: 7 pages, 2 added references, some added discussion, no changes in physics conclusion
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