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

Understand

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.