Higher dimensional black holes in external magnetic fields

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.