Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity

TL;DR

This paper derives the electromagnetic vector potential for hairy black holes in Horndeski gravity and analyzes charged-particle dynamics, revealing conditions for chaos versus order in curved spacetime.

Contribution

It extends the Wald vector potential to nonvacuum, hairy black holes in Horndeski gravity and applies advanced numerical methods to study particle motion and chaos.

Findings

Charged-particle motion exhibits chaotic behavior in certain magnetic field configurations.

Recurrence analysis effectively distinguishes between regular and chaotic dynamics.

The derived vector potential generalizes known solutions to modified gravity scenarios.

Abstract

The Wald vector potential is an exact solution of the source-less Maxwell equations regarding an electromagnetic field of a vacuum uncharged black hole like the Kerr background black hole in an asymptotically uniform magnetic field. However, it is not if the black hole is a nonvacuum solution in a theory of modified gravity with extra fields or a charged Kerr-Newman spacetime. To satisfy the source-less Maxwell equations in this case, the Wald vector potential must be modified and generalized appropriately. Following this idea, we derive an expression for the vector potential of an electromagnetic field surrounding a hairy black hole in the Horndeski modified gravity theory. Explicit symplectic integrators with excellent long-term behaviour are used to simulate the motion of charged particles around the hairy black hole immersed in the external magnetic field. The recurrence plot method based on the recurrence quantification analysis uses diagonal structures parallel to the main diagonal to show regular dynamics, but adopts no diagonal structures to indicate chaotic dynamics. The method is efficient to detect chaos from order in the curved spacetime, as the Poincare map and the fast Lyapunov indicator are.