Extremal Vanishing Horizon Kerr-AdS Black Holes at Ultraspinning Limit

By utilizing the ultraspinning limit we generate a new class of extremal vanishing horizon (EVH) black holes in odd dimensions ($d\geq5$). Starting from the general multi-spinning Kerr-AdS metrics, we show the EVH limit commutes with the ultraspinning limit, in which the resulting solutions possess a non-compact but finite area manifold for all $(t,r\neq r_+)=const.$ slices. We also demonstrate the near horizon geometries of obtained ultraspinning EVH solutions contain an AdS$_3$ throats, where it would be a BTZ black hole in the near EVH cases. The commutativity of the ultraspinning and near horizon limits for EVH solutions is confirmed as well. Furthermore, we discuss only the five-dimensional case near the EVH point can be viewed as a super-entropic black hole. We also show that the thermodynamics of the obtained solutions agree with the BTZ black hole. Moreover we investigate the EVH/CFT proposal, demonstrating the entropy of $2$d dual CFT and Bekenstein-Hawking entropy are equivalent.Comment: 29 pages, 3 figures, references added, typos corrected, revised version to match published versio

Three Theorems on Near Horizon Extremal Vanishing Horizon Geometries

EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle 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 Einstein-Maxwell-dilaton-Lambda 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 d-3 dimensional part. (3) These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.Comment: 5 page

Near Horizon Structure of Extremal Vanishing Horizon Black Holes

We study the near horizon structure of Extremal Vanishing Horizon (EVH) black holes, extremal black holes with vanishing horizon area with a vanishing one-cycle on the horizon. We construct the most general near horizon EVH and near-EVH ansatz for the metric and other fields, like dilaton and gauge fields which may be present in the theory. We prove that (1) the near horizon EVH geometry for generic gravity theory in generic dimension has a three dimensional maximally symmetric subspace; (2) if the matter fields of the theory satisfy strong energy condition either this 3d part is AdS$_3$, or the solution is a direct product of a locally 3d flat space and a $d-3$ dimensional part; (3) these results extend to the near horizon geometry of near-EVH black holes, for which the AdS$_3$ part is replaced with BTZ geometry. We present some specific near horizon EVH geometries in 3, 4 and 5 dimensions for which there is a classification. We also briefly discuss implications of these generic results for generic (gauged) supergravity theories and also for the thermodynamics of near-EVH black holes and the EVH/CFT proposal.Comment: 26 page

On Complexity for Higher Derivative Gravities

Using "complexity=action" proposal we study complexity growth of certain gravitational theories containing higher derivative terms. These include critical gravity in diverse dimensions. One observes that the complexity growth for neutral black holes saturates the proposed bound when the results are written in terms of physical quantities of the model. We will also study effects of shock wave to the complexity growth where we find that the presence of massive spin-2 mode slows down the rate of growth.Comment: 18 pages, 3 figures, journal versio