The particle surface of spinning test particles

TL;DR

This paper introduces a new quasi-local definition for studying circular orbits of spinning test particles, applicable to both photons and massive particles in various spacetimes, including dynamical ones.

Contribution

It proposes an alternative quasi-local definition for particle orbits that extends to spinning particles and dynamical spacetimes, surpassing traditional effective potential methods.

Findings

The definition reproduces known photon surfaces in spherically symmetric spacetimes.

It generalizes to pole-dipole particles and matches effective potential results in static cases.

Applicable to dynamical spacetimes, unlike traditional methods.

Abstract

In this work, inspired by the definition of the photon surface given by Claudel, Virbhadra, and Ellis, we give an alternative quasi-local definition to study the circular orbits of single-pole particles. This definition does not only apply to photons but also to massive point particles. For the case of photons in spherically symmetric spacetime, it will give a photon surface equivalent to the result of Claudel, Virbhadra, and Ellis. Meanwhile, in general static and stationary spacetime, this definition can be regarded as a quasi-local form of the effective potential method. However, unlike the effective potential method which can not define the effective potential in dynamical spacetime, this definition can be applied to dynamical spacetime. Further, we generalize this definition directly to the case of pole-dipole particles. In static spherical symmetry spacetime, we verify the correctness of this generalization by comparing the results obtained by the effective potential method.