# Charged particle motion around a quasi-Kerr compact object immersed in an external magnetic field

## TL;DR

This paper investigates the motion of charged particles around a quasi-Kerr compact object in an external magnetic field, deriving effective potentials, ISCO properties, and energy outcomes to understand their dynamics and constraints on deformation parameters.

## Contribution

It introduces a detailed analysis of charged particle dynamics around a quasi-Kerr object in magnetic fields, including effective potentials, ISCO behavior, and collision energies, with new constraints on deformation parameters.

## Key findings

- Derived electromagnetic field components using the Wald method.
- Calculated the effective potential for charged particles around a quasi-Kerr object.
- Constrained the deformation parameter based on ISCO radius measurements.

## Abstract

We explore the electromagnetic fields around a quasi-Kerr compact object assuming it is immersed in an external asymptotically uniform magnetic field. Using the Wald method, components of the electromagnetic field in orthonormal basis have been obtained. We explore the charged particle motion around deformed Kerr compact objects in the presence of external asymptotically uniform magnetic fields. Using the Hamilton-Jacobi equation, we obtain the effective potential expression for the charged particle surrounding a quasi-Kerr compact object immersed in an external magnetic field. It is also derived the dependence of innermost stable circular orbits (ISCOs) from the magnetic and deformation parameters for charged particles motion around a rotating quasi-Kerr compact object. Comparison with ISCO radius measurements has provided the constraint to the deformation parameter as $\epsilon \gtrsim -0.012$. The center of mass (CM) energy of the colliding particles in several physically interesting cases has been studied.