Hidden Symmetries and Gyromagnetic Ratio of Kerr-Newman Black Holes in $f(R)$ Gravity

TL;DR

This paper investigates hidden symmetries and the gyromagnetic ratio of Kerr-Newman black holes in $f(R)$ gravity, revealing that the universal gyromagnetic ratio persists and connecting symmetries to spacetime separability.

Contribution

It derives Killing and Killing-Yano tensors in $f(R)$ gravity and shows the gyromagnetic ratio remains at 2, extending known black hole properties to modified gravity theories.

Findings

Gyromagnetic ratio remains at g=2 in $f(R)$ gravity.

Hidden symmetries facilitate Hamilton-Jacobi equation separation.

Connections between symmetries and spacetime structure are established.

Abstract

We explore hidden symmetries in electrically charged, four-dimensional rotating Kerr-Newman black hole within $f(R)$ gravity. By deriving the Killing and Killing-Yano tensors, we establish their role in the spacetime structure. The gyromagnetic ratio is calculated and shown to retain its universal value of $g = 2$, consistent with all four-dimensional black holes. These findings show that the gyromagnetic ratio remains consistent in this modified gravity setting. Moreover, they highlight the connection between hidden symmetries and the ability to separate the Hamilton-Jacobi equation in $f(R)$ gravity. This work advances the study of black holes in modified gravity, offering implications for both theoretical frameworks and observational cosmology, such as gravitational wave analyses.