Mass of Kerr-Newman black holes in an external magnetic field

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.

Thermodynamics of charged, rotating, and accelerating black holes

“…The key insight in our approach is to consider the extended first law (1) with the additional terms that allow us to vary the tension. This is in direct contrast to the approach presented in [19] (see also [32]) where one tension is fixed (at zero) and all remaining parameters are permitted to vary. This is perplexing, as a first law without varying tension then has reduced cohomogeneity, i.e.…”

Black hole thermodynamics with conical defects

“…Given the central importance of black hole thermodynamics in theoretical gravity, it is surprising that until recently only the thermodynamics of relatively simply systems had been explored. Although our catalog of exact black hole solutions is limited (mostly) to isolated gravitating systems, there is a class of intriguing exceptions, given by axisymmetric solutions to the Einstein equations [12,13], including axisymmetric multiple black holes [14][15][16][17][18], black holes in magnetic flux tubes (including a study of thermodynamics) [19][20][21], and most pertinently for our discussion, the accelerating black hole. This last example has an exact solution known as the C-metric [22,23], corresponding to a black hole with a conical deficit emerging from one pole, or unequal conical deficits emerging from each pole.…”

Accelerating black hole chemistry

“…Not only have we proved a new Entropy Inequality for black holes with conical deficits, but by writing down a Christodoulou-Ruffini type of mass formula, we have now expressed the mass of a four-dimensional black hole that includes two new charges: ∆ and C, or, the average deficit and acceleration. It would be interesting to understand how our expressions relate to those in [34] for an unconfined magnetic flux tube through a black hole. One possibly disturbing aspect of the exothermic impact of acceleration is that it seems to diverge as the pressure tends to zero.…”