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Updated: Feb 11, 2026

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Published on: December 9, 2011
Gravity and the Spin-2 Planar Schrödinger Equation
Eric A Bergshoeff1, Jan Rosseel2, Paul K Townsend3
1Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands and Institut de Physique Théorique Philippe Meyer, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
Abstract:
A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2+1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3+1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.
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