Glued massive particles surfaces

TL;DR

This paper introduces a new concept of glued massive particle surfaces in spacetimes with symmetries, extending photon surface ideas to massive charged particles, with potential applications in black hole physics and spacetime geometry.

Contribution

It generalizes photon surfaces to massive charged particles, defines glued massive particle surfaces, and explores their geometric properties and applications in integrable spacetimes.

Findings

Defined glued massive particle surfaces in spacetimes with isometries.

Demonstrated the relationship between these surfaces and Killing tensors.

Provided examples illustrating the geometric properties and potential applications.

Abstract

A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These surfaces join worldlines parametrized by a family of independent conserved quantities and naturally arise in integrable spacetimes. We describe the basic geometric properties of such surfaces and their relationship to slice-reducible Killing tensors, illustrating all concepts with a number of examples. Massive particle surfaces have potential applications in the context of uniqueness theorems, Penrose inequalities, integrability, and the description of black-hole shadows in streams of massive charged particles or photons in a medium with an effective mass and charge.