Modified light-cylinder and centrifugal acceleration in Schwarzschild geometry

TL;DR

This paper investigates how gravity alters the concept of a light cylinder and electron acceleration near black holes, revealing a modified light cylinder shape and maximum electron energies considering various radiation limits.

Contribution

It introduces a modified light cylinder in Schwarzschild spacetime and analyzes the maximum electron energies accounting for gravitational effects and radiation losses.

Findings

The light cylinder becomes a non-cylindrical surface in Schwarzschild geometry.

Maximum electron energies are constrained by inverse Compton, curvature, and synchrotron radiation.

Gravity significantly impacts particle acceleration near black holes.

Abstract

We examine the motion of an electron constrained to follow a magnetic field line near a primordial sub-stellar mass black hole. Earlier studies treated the problem in flat (Minkowski) spacetime, yielding qualitatively correct results and introducing a light cylinder (LC), a hypothetical surface where the linear velocity of rotation equals the speed of light. However, this picture changes significantly when gravity is included. By analyzing the electron's dynamics in the Schwarzschild metric, we obtain a modified light cylinder (MLC) whose geometry no longer resembles a cylinder. We then determine the maximum energies attainable by the electrons under the limiting effects of inverse Compton scattering, curvature radiation, and synchrotron radiation.