  We examine several aspects of black hole horizon physics using the
Melvin-Kerr-Newman (MKN) family of spacetimes. Roughly speaking these are black
holes immersed in a distorting background magnetic field and unlike the
standard Kerr-Newman (KN) family they are not asymptotically flat. As exact
solutions with horizons that can be highly distorted relative to KN, they
provide a good testbed for ideas about and theorems constraining black hole
horizons.
  We explicitly show that MKN horizons with fixed magnetic field parameter may
be uniquely specified by their area, charge and angular momentum and that the
charge and angular momentum are bound by horizon area in the same way as for
KN. As expected, extremal MKN horizons are geometrically isomorphic to extremal
KN horizons and the geometric distortion of near-extremal horizons is
constrained by their proximity to extremality. At the other extreme,
Melvin-Schwarzschild (MS) solutions may be infinitely distorted, however for
intermediate cases any non-zero charge or angular momentum restricts
distortions to be finite. These properties are in agreement with known theorems
but are seen to be satisfied in interesting and non-trivial ways.
