Gravity and the spin-2 planar Schroedinger equation

Abstract

A Schroedinger equation proposed for the GMP gapped spin-2 mode of fractional Quantum Hall states is found from a novel non-relativistic 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 non-linear Einstein equations, a confining harmonic oscillator potential for the individual particles.

5 pages. Additional references, with discussion, in v2, plus improved analysis of parity violation

References in corpus (5)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Newtonian Gravity and the Bargmann Algebra
• Theory of Nematic Fractional Quantum Hall State
• Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group

Cited by in corpus (13)

• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Exotic Massive 3D Gravity
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Quantum probing of null-singularities
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Weyl-Lorentz-U(1)-invariant symmetric teleparallel gravity in three dimensions
• Emerging (2+1)D massive graviton in graphene-like systems
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Is the cosmological constant an eigenvalue?