# Charged particle motion and electromagnetic field in $\gamma$ spacetime

## TL;DR

This paper investigates the motion of charged particles and electromagnetic fields in the gamma spacetime, a static, axially symmetric solution of Einstein's equations, revealing high-energy collisions near singularities that differ from black hole behavior.

## Contribution

It analyzes particle dynamics and collisions in gamma spacetime, highlighting differences from Schwarzschild black holes and proposing a method to distinguish such sources.

## Key findings

- High-energy particle collisions near singular surfaces in gamma spacetime.
- Contrasts between gamma spacetime and black hole collision outcomes.
- Potential observational signatures to differentiate gamma sources from black holes.

## Abstract

We consider the electromagnetic field occurring in the background of a static, axially symmetric vacuum solution of Einstein's field equations immersed in an external magnetic field. The solution, known as the $\gamma$ metric (or Zipoy-Voorhees), is related to the Schwarzschild spacetime through a real positive parameter $\gamma$ that describes its departure from spherical symmetry. We study the motion of charged and uncharged particles in this spacetime and particle collision in the vicinity of the singular surface and compare with the corresponding result for Schwarzschild. We show that there is a sharp contrast with the black hole case; in particular, in the prolate case ($\gamma<1$) particle collision can occur with an arbitrarily high center of mass energy. This mechanism could in principle allow one to distinguish such a source from a black hole.