On the Bekenstein-Hawking area law for black objects with conical singularities

We argue that, when working with the appropriate set of thermodynamical variables, the Bekenstein-Hawking law still holds for asymptotically flat black objects with conical singularities. The mass-energy which enters the first law of thermodynamics does not, however, coincide with the ADM mass; it differs from the latter by the energy associated with the conical singularity, as seen by an asymptotic, static observer. These statements are supported by a number of examples: the Bach-Weyl (double-Schwarzschild) solution, its dihole generalisation in Einstein-Maxwell theory and the five dimensional static black ring.