Higher dimensional black holes in external magnetic fields

We apply a Harrison transformation to higher dimensional asymptotically flatblack hole solutions, which puts them into an external magnetic field. First,we magnetize the Schwarzschild-Tangherlini metric in arbitrary spacetimedimension n>=4. The thus generated exact solution of the Einstein-Maxwellequations describes a static black hole immersed in a Melvin "fluxbrane", andgeneralizes previous results by Ernst for the case n=4. The magnetic fielddeforms the shape of the event horizon, but the total area (as a function ofthe mass) and the thermodynamics remain unaffected. The amount of flux througha one-dimensional loop on the horizon exhibits a maximum for a finite value ofthe magnetic field strength, and decreases for larger values. In theAichelburg-Sexl ultrarelativistic limit, the magnetized black hole becomes animpulsive gravitational wave propagating in the Melvin background. Furthermore,we discuss possible applications of a similar Harrison transformation torotating black objects. This enables us to magnetize the Myers-Perry hole andthe (dipole) Emparan-Reall ring at least in the special case when the vectorpotential is parallel to a nonrotating Killing field. In particular, dipolerings may be held in equilibrium even when their spin vanishes, thusdemonstrating (infinite) non-uniqueness of magnetized static uncharged blackholes in five dimensions. Physical properties of such rings are discussed.Comment: 1+22 pages, 1 figure. v2: added Appendix B (on magnetized static rings), one new reference, minor changes in the text. v3: discussion on static rings extended and incorporated into the main text, transformation to the coordinates of Ref. [42] (for extremal static rings) presented in new Appendix B, two new references, other minor changes. To appear in JHE