SMOOTHNESS OF THE HORIZONS OF MULTI-BLACK-HOLE SOLUTIONS

In a recent paper it was suggested that some multi-black-hole solution s in five or more dimensions have horizons that are not smooth. These black hole configurations are solutions to d-dimensional Einstein grav ity (with no dilaton) and are extremely charged with a magnetic-type ( d - 2)-form. In this work we investigate these solutions further. It i s shown that although the curvature is bounded as the horizon of one o f the black holes is approached, some derivatives of the curvature are not. This shows that the metric is not C-infinity, but rather is only C-k with k finite. These solutions are static so their lack of smooth ness cannot be attributed to the presence of radiation.