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The Gödel-Schrödinger spacetime and stringy chronology protection

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Abstract

We show that the null Melvin map applied to a rotational isometry of global anti-de Sitter space produces a spacetime with properties analogous to both the Gödel and Schrödinger geometries. The isometry group of this Gödel-Schrödinger spacetime is appropriate to provide a holographic dual for the same non-relativistic conformal theory as the ordinary Schrödinger geometry, but defined on a sphere. This spacetime also possesses closed timelike curves outside a certain critical radius. We show that a holographic preferred screen for an observer at the origin sits at an interior radius, suggesting that a holographic dual description would only require the chronologically consistent region. Additionally, giant graviton probe branes experience repulson-type instabilities in the acausal region, suggesting a condensation of branes will modify the pathological part of the geometry to remove the closed timelike curves.

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  1. Charles Max Brown

    Present address: Department of Mathematics and Physics, Kentucky State University, Carver Hall 131, 400 E. Main St., Frankfort, KY, 40601, U.S.A.

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  1. Department of Physics, University of Colorado, 390 UCB, Boulder, CO, 80309, U.S.A.

    Charles Max Brown & Oliver DeWolfe

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Correspondence to Oliver DeWolfe.

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ArXiv ePrint: 1110.3840

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Brown, C.M., DeWolfe, O. The Gödel-Schrödinger spacetime and stringy chronology protection. J. High Energ. Phys. 2012, 32 (2012). https://doi.org/10.1007/JHEP01(2012)032

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