Geodesic deviation to all orders via a tangent bundle formalism

2025/09/28 by Kim, Joon-Hwi · 3 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2509.23600

Abstract

We establish an in-in formalism for geodesic deviation as an alternative to Synge calculus, based on a covariant calculus of differential forms in tangent bundle. This derives the exact Lagrangian and equations governing the finite geodesic deviation between a free-falling test particle and an arbitrary observer, in terms of infinite sums whose coefficients are products of binomial coefficients. Explicit expressions are provided up to tenth order, finding agreements with the previous fourth-order result.

Citations

• Note on the Kerr Spinning-Particle Equations of Motion
• Worldline formalism in phase space
• Fermion Geometry and the Renormalization of the Standard Model Effective Field Theory
• The Large Scale Structure of Space-Time
• Spacetime and Geometry
• Strings in Background Fields
• Tensor Calculus
• The Motion of Point Particles in Curved Spacetime
• Spinning test-particles in general relativity. I
• On the Deviation of Geodesics and Null-Geodesics, Particularly in Relation to the Properties of Spaces of Constant Curvature and Indefinite Line-Element

Cited by

• Note on the Kerr Spinning-Particle Equations of Motion
• Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics
• Double copy and the double Poisson bracket

Related

• On the Deviation of Geodesics and Null-Geodesics, Particularly in Relation to the Properties of Spaces of Constant Curvature and Indefinite Line-Element
• Deviation equations in spaces with a transport along paths
• First order deviation equations in spaces with a transport along paths
• Solutions of the Equations of Geodesic Deviation for Static Spherical Symmetric Space‐times
• Deviation differential equations. Jacobi fields