Plane Gravitational Waves and Flat Space in Loop Quantum Gravity

  • Franz HinterleitnerEmail author
  • Seth Major
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 157)


Classically a system of arbitrary plane gravitational waves propagating in the same or opposite directions can be restricted by first-class constraints to unidirectional waves, which travel without dispersion on a flat background. The unidirectionality constraints are formulated as well-defined Loop Quantum Gravity operators, together with criteria for an anomaly-free implantation, which is crucial for the occurrence or non-occurrence of dispersion, and more generally, of local Lorentz invariance violations due to (loop) quantum effects. By a set of further first-class constraints of the same kind we construct a quantum model of a no-wave state, i.e. of empty space.


Poisson Bracket Loop Quantum Gravity Flat Space Hamiltonian Constraint Flux Operator 
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  1. 1.
    Bojowald, M., Swiderski, R.: Spherically symmetric quantum geometry: Hamiltonian constraint. Class. Quantum Grav. 23, 2129 (2006). doi: 10.1088/0264-9381/23/6/015 ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Banerjee, K., Date, G.: Loop quantization of polarized Gowdy model on \(T^3\): kinematical states and constraint operators. Class. Quantum Grav. 25, 145004 (2008). doi:  10.1088/0264-9381/25/14/145004 ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hinterleitner, F., Major, S.: Towards loop quantization of plane gravitational waves. Class. Quantum Grav. 29, 065019 (2012). doi: 10.1088/0264-9381/29/6/065019 ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ehlers, J., Kundt, W.: Exact solutions of gravitational field equations. In: Witten, L. (ed.) Gravitation: An Introduction to Current Research, pp. 33.6, 35.9. Wiley, New York (1962).Google Scholar
  5. 5.
    Thiemann, T.: Modern Canonical Quantum General Relativity. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  6. 6.
    Rovelli, C.: Quantum Gravity. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Theoretical Physics and AstrophysicsMasaryk UniversityBrnoCzech Republic
  2. 2.Department of PhysicsHamilton CollegeClintonUSA

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