Mass of Kerr-Newman Black Holes in an external magnetic field

TL;DR

This paper clarifies the thermodynamics of Kerr-Newman black holes in magnetic fields, defining a unique mass that aligns with the Christodoulou-Ruffini mass and extends black hole thermodynamics to magnetized environments.

Contribution

It introduces a well-defined mass for magnetized Kerr-Newman black holes and clarifies their thermodynamic relations, extending classical black hole thermodynamics to magnetic field contexts.

Findings

Mass coincides with Christodoulou-Ruffini mass in absence of magnetic field

First law and Smarr formula are clarified for magnetic black holes

Thermodynamic potentials are defined for magnetized black holes

Abstract

The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular momentum and electric charge.