Dynamics for Spin-$1/2$ Particles in Einstein-Gauss-Bonnet Gravity

TL;DR

This paper develops a quantum dynamical framework for spin-$1/2$ particles in Einstein-Gauss-Bonnet black-hole spacetime, revealing curvature-dependent quantum corrections to particle motion.

Contribution

It constructs the Dirac Hamiltonian in EGB gravity and derives explicit quantum equations of motion, highlighting higher-curvature effects on particle dynamics.

Findings

Force operator includes Gauss-Bonnet coupling corrections

Radial force deviates from GR in strong-field regimes

Quantum effects modify classical geodesic motion

Abstract

I investigate the quantum dynamics of a spin-$1/2$ particle in a static, spherically symmetric Einstein-Gauss-Bonnet (EGB) black-hole spacetime within the Hamiltonian framework. Starting from the Dirac equation in curved spacetime, formulated via the tetrad formalism and the associated spin connection, we construct the corresponding Dirac Hamiltonian in the EGB background. Using this Hamiltonian, we derive the Heisenberg equations of motion for the position and momentum operators, obtaining explicit expressions for the velocity and force operators. This operator-based approach provides a direct description of particle dynamics beyond classical geodesic motion, incorporating both relativistic and quantum effects. We show that the resulting force operator contains corrections explicitly dependent on the Gauss-Bonnet coupling parameter $\xi$, which encode higher-curvature modifications of the gravitational interaction at the quantum level. In particular, the effective radial force deviates from its general relativistic counterpart by terms that become significant in the strong-field regime.