On Classification of Geometries with SO(2,2) Symmetry

Motivated by the Extremal Vanishing Horizon (EVH) black holes, their near horizon geometry and the EVH/CFT proposal, we construct and classify solutions with (local) SO(2,2) symmetry to four and five dimensional Einstein-Maxwell-Dilaton (EMD) theory with positive, zero or negative cosmological constant Lambda, the EMD-$\Lambda$ theory, and also $U(1)^4$ gauged supergravity in four dimensions and $U(1)^3$ gauged supergravity in five dimensions. In four dimensions the geometries are warped product of AdS3 with an interval or a circle. In five dimensions the geometries are of the form of warped product of AdS3 and a 2d surface $\Sigma_2$. For the Einsten-Maxwell-$\Lambda$ theory we prove that $\Sigma_2$ should have a U(1) isometry, a rigidity theorem in this class of solutions. We also construct all d dimensional Einstein vacuum solutions with $SO(2,2) \times U(1)^{d-4}$ or $SO(2,2) \times SO(d-3)$ isometry.Comment: 26 pages, updated to 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

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

Can the string scale be related to the cosmic baryon asymmetry?

In a previous work, a mechanism was presented by which baryon asymmetry can be generated during inflation from elliptically polarized gravitons. Nonetheless, the mechanism only generated a realistic baryon asymmetry under special circumstances which requires an enhancement of the lepton number from an unspecified GUT. In this note we provide a stringy embedding of this mechanism through the Green-Schwarz mechanism, demonstrating that if the model-independent axion is the source of the gravitational waves responsible for the lepton asymmetry, one can observationally constrain the string scale and coupling.Comment: 12 Pages, typo corrected in the tex