# Classical and Quantum Aspects of Particle Propagation in External Gravitational Fields

## TL;DR

This paper explores how classical and quantum particles propagate in external gravitational fields, focusing on the effects of metric deviations and a vector potential on particle behavior, including dispersion, tunneling, and radiation.

## Contribution

It introduces a framework combining covariant wave equations with dual gravitational potentials, revealing their combined influence on particle dynamics and quantum phenomena.

## Key findings

- Kλ affects particle dispersion relations
- Particles exhibit modified motion and tunneling behaviors
- Flux quantization is influenced by gravitational potentials

## Abstract

In the study of covariant wave equations, linear gravity manifests itself through the metric deviation $\gamma_{\mu\nu}$ and a two-point vector potential $K_{\lambda}$ itself constructed from $\gamma_{\mu\nu}$ and its derivatives. The simultaneous presence of the two gravitational potentials is non contradictory. Particles also assume the character of quasiparticles and $K_{\lambda}$ carries information about the matter with which it interacts. We consider the influence of $K_{\lambda}$ on the dispersion relations of the particles involved, the particles' motion, quantum tunneling through a horizon, radiation, energy-momentum dissipation and flux quantization. % No {\it REVTEX} limit to number of lines.