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We study the near horizon structure of Extremal Vanishing Horizon (EVH) blackholes, extremal black holes with vanishing horizon area with a vanishingone-cycle on the horizon. We construct the most general near horizon EVH andnear-EVH ansatz for the metric and other fields, like dilaton and gauge fieldswhich may be present in the theory. We prove that (1) the near horizon EVHgeometry for generic gravity theory in generic dimension has a threedimensional maximally symmetric subspace; (2) if the matter fields of thetheory satisfy strong energy condition either this 3d part is AdS$_3$, or thesolution is a direct product of a locally 3d flat space and a $d-3$ dimensionalpart; (3) these results extend to the near horizon geometry of near-EVH blackholes, for which the AdS$_3$ part is replaced with BTZ geometry. We presentsome specific near horizon EVH geometries in 3, 4 and 5 dimensions for whichthere is a classification. We also briefly discuss implications of thesegeneric results for generic (gauged) supergravity theories and also for thethermodynamics of near-EVH black holes and the EVH/CFT proposal.

Near Horizon Structure of Extremal Vanishing Horizon Black Holes