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Paper IPM / P / 14188  


Abstract:  
EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing onecycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are EinsteinMaxwelldilatonLambda theories, and gauged or ungauged supergravity theories with U(1) Maxwell fields. Our three theorems are: (1) The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2) If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d3 dimensional part. (3) These results extend to the near horizon geometry of nearEVH black holes, for which the AdS3 part is replaced with BTZ geometry.
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