Dynamics for Spin-1/2 Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case
Abstract
In this work, I investigate the non-relativistic quantum dynamics of spin-1/2 particles in Einstein-Gauss-Bonnet (EGB) gravity and establish a direct connection between higher-curvature corrections, fermionic dynamics, and the phenomenology of compact objects. Starting from the Dirac Hamiltonian in a static, spherically symmetric EGB spacetime, we perform a Fold-Wouthuysen transformation and derive the effective Hamiltonian, including relativistic kinetic, gravitational, spin-orbit, and higher-curvature contributions. Heisenberg equations are then used to obtain the dynamics of velocity, force, and spin, revealing explicit EGB corrections for both translational motion and spin transport. In particular, the spin-orbit sector induces a modified precession frequency whose fractional deviation from general relativity scales as δΩ=−4(ξ/M2)(M/ρ)3, providing a clear dimensionless signature of the Gauss-Bonnet coupling. Through Ehrenfest's theorem, we also establish the correspondence between the dynamics of quantum operators and their semiclassical gravitational limit. As an astrophysical application, we consider the stellar-mass black hole A0620-00 and show that prospective relative sensitivities in spin precession on the order of 10−3 to 10−4 can probe Gauss-Bonnet couplings in the range of approximately 106 to 108 m2, depending on the orbital radius. This result identifies fermionic spin precession as a complementary channel for testing gravity with higher-curvature corrections and provides a quantum-mechanical framework connecting modified gravitational dynamics to precision phenomenology in strong-gravity regimes.
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BibTeX
@misc{maciel2026dynamics,
title = {{Dynamics for Spin-$1/2$ Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case}},
author = {E. Maciel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12279},
eprint = {2609.12279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12279},
}
RIS
TY - UNPB
TI - Dynamics for Spin-1/2 Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case
AU - E. Maciel
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.12279
UR - https://arxiv.org/abs/2609.12279
AB - In this work, I investigate the non-relativistic quantum dynamics of spin-1/2 particles in Einstein-Gauss-Bonnet (EGB) gravity and establish a direct connection between higher-curvature corrections, fermionic dynamics, and the phenomenology of compact objects. Starting from the Dirac Hamiltonian in a static, spherically symmetric EGB spacetime, we perform a Fold-Wouthuysen transformation and derive the effective Hamiltonian, including relativistic kinetic, gravitational, spin-orbit, and higher-curvature contributions. Heisenberg equations are then used to obtain the dynamics of velocity, force, and spin, revealing explicit EGB corrections for both translational motion and spin transport. In particular, the spin-orbit sector induces a modified precession frequency whose fractional deviation from general relativity scales as δ_Ω=−4(ξ/M^2)(M/ρ)^3, providing a clear dimensionless signature of the Gauss-Bonnet coupling. Through Ehrenfest's theorem, we also establish the correspondence between the dynamics of quantum operators and their semiclassical gravitational limit. As an astrophysical application, we consider the stellar-mass black hole A0620-00 and show that prospective relative sensitivities in spin precession on the order of 10^−3 to 10^−4 can probe Gauss-Bonnet couplings in the range of approximately 10^6 to 10^8 m^2, depending on the orbital radius. This result identifies fermionic spin precession as a complementary channel for testing gravity with higher-curvature corrections and provides a quantum-mechanical framework connecting modified gravitational dynamics to precision phenomenology in strong-gravity regimes.
ER -