On Integrability of spinning particle motion in higher-dimensional black hole spacetimes

Abstract

We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing--Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et. al. [hep-th/0611083] on complete integrability of geodesic motion in these spacetimes.

Version 2: revised version, added references. 5 pages, no figures

References in corpus (7)

• General Kerr-NUT-AdS Metrics in All Dimensions
• Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
• Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
• Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions
• SUSY in the Spacetime of Higher-Dimensional Rotating Black Holes

Cited by in corpus (27)

• Black holes, hidden symmetries, and complete integrability
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Maxwell's Equations in the Myers-Perry Geometry
• Hamilton-Jacobi equation for spinning particles near black holes
• Killing(-Yano) Tensors in String Theory
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• Complete set of quasi-conserved quantities for spinning particles around Kerr
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Excitations of the Myers-Perry Black Holes
• Spinning particle orbits around a black hole in an expanding background
• Scalar fields on λ-deformed cosets
• On Integrability of the Geodesic Deviation Equation
• Exotic Black Hole Thermodynamics in Third-Order Lovelock Gravity
• Uses of Killing and Killing-Yano Tensors
• Hidden Symmetries and Geodesics of Kerr spacetime in Kaluza-Klein Theory
• On Conserved Quantities for the Free Motion of Particles with Spin
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• Motion of Spinning Particles around Black Holes
• Hidden Symmetries of the Dirac equation in curved spacetime
• Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
• Separation of variables in the WZW models
• Conformally equivariant quantization for spinning particles
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane
• The geodesic structure of BPS one-branes in five dimensions