# Generic rotating regular black holes in general relativity coupled to nonlinear electrodynamics

## TL;DR

This paper constructs and analyzes new rotating regular black hole solutions in general relativity coupled with nonlinear electrodynamics, exploring their horizons, geodesics, and particle motion, revealing differences from Kerr black holes.

## Contribution

It introduces a class of generic rotating regular black holes derived from spherically symmetric solutions, analyzing their properties and geodesic structure, including the effects of nonlinear electrodynamics.

## Key findings

- Weak and strong energy conditions are violated inside Cauchy horizons.
- The structure of circular geodesics and epicyclic frequencies differ from Kerr black holes.
- The frequencies of particle oscillations are always smaller than in Kerr spacetime.

## Abstract

We construct regular rotating black hole and no-horizon spacetimes based on the recently introduced spherically symmetric generic regular black hole spacetimes related to electric or magnetic charge under nonlinear electrodynamics coupled to general relativity that for special values of the spacetime parameters reduce to the Bardeen and Hayward spacetimes. We show that the weak and strong energy conditions are violated inside the Cauchy horizons of these generic rotating black holes. We give the boundary between the rotating black hole and no-horizon spacetimes and determine the black hole horizons and the boundary of the ergosphere. We introduce the separated Carter equations for the geodesic motion in these rotating spacetimes. For the most interesting new class of the regular spacetimes, corresponding for magnetic charges to the Maxwell field in the weak field limit of the nonlinear electrodynamics, we determine the structure of the circular geodesics and discuss their properties. We study the epicyclic motion of a neutral particle moving along the stable circular orbits around the "Maxwellian" rotating regular black holes. We show that epicyclic frequencies measured by the distant observers and related to the oscillatory motion of the neutral test particle along the stable circular orbits around the rotating singular and regular Maxwellian black holes are always smaller than ones in the Kerr spacetime.