Higher dimensional black holes in external magnetic fields

TL;DR

This paper extends the Harrison transformation to higher-dimensional black holes, creating exact solutions with external magnetic fields, and explores their properties, including horizon deformation, flux behavior, and applications to rotating black objects.

Contribution

It generalizes the magnetization process to higher dimensions and applies it to various black hole solutions, revealing new equilibrium states and non-uniqueness in five dimensions.

Findings

Magnetized black holes in higher dimensions maintain horizon area and thermodynamics.

Flux through the horizon has a maximum at finite magnetic field strength.

Magnetized black rings can be in equilibrium even without spin.

Abstract

We apply a Harrison transformation to higher dimensional asymptotically flat black hole solutions, which puts them into an external magnetic field. First, we magnetize the Schwarzschild-Tangherlini metric in arbitrary spacetime dimension n>=4. The thus generated exact solution of the Einstein-Maxwell equations describes a static black hole immersed in a Melvin "fluxbrane", and generalizes previous results by Ernst for the case n=4. The magnetic field deforms the shape of the event horizon, but the total area (as a function of the mass) and the thermodynamics remain unaffected. The amount of flux through a one-dimensional loop on the horizon exhibits a maximum for a finite value of the magnetic field strength, and decreases for larger values. In the Aichelburg-Sexl ultrarelativistic limit, the magnetized black hole becomes an impulsive gravitational wave propagating in the Melvin background. Furthermore, we discuss possible applications of a similar Harrison transformation to rotating black objects. This enables us to magnetize the Myers-Perry hole and the (dipole) Emparan-Reall ring at least in the special case when the vector potential is parallel to a nonrotating Killing field. In particular, dipole rings may be held in equilibrium even when their spin vanishes, thus demonstrating (infinite) non-uniqueness of magnetized static uncharged black holes in five dimensions. Physical properties of such rings are discussed.