Conformal Symmetry of a Black Hole as a Scaling Limit: A Black Hole in an Asymptotically Conical Box

We show that the previously obtained subtracted geometry of four-dimensional asymptotically flat multi-charged rotating black holes, whose massless wave equation exhibit $SL(2,\R) × SL(2,\R) × SO(3)$ symmetry may be obtained by a suitable scaling limit of certain asymptotically flat multi-charged rotating black holes, which is reminiscent of near-extreme black holes in the dilute gas approximation. The co-homogeneity-two geometry is supported by a dilation field and two (electric) gauge-field strengths. We also point out that these subtracted geometries can be obtained as a particular Harrison transformation of the original black holes. Furthermore the subtracted metrics are asymptotically conical (AC), like global monopoles, thus describing "a black hole in an AC box". Finally we account for the the emergence of the $SL(2,\R) × SL(2,\R) × SO(3)$ symmetry as a consequence of the subtracted metrics being Kaluza-Klein type quotients of $ AdS_3× 4 S^3$. We demonstrate that similar properties hold for five-dimensional black holes.