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

Abstract

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.

arXiv comment26 pages, updated to published version

References in corpus (25)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• The Thermodynamics of Black Holes
• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Black Holes in Higher Dimensions
• Near-horizon symmetries of extremal black holes
• Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics
• Classification of near-horizon geometries of extremal black holes
• A classification of near-horizon geometries of extremal vacuum black holes
• Superconformal Gauge Theories and Non-Critical Superstrings
• The Role of Dipole Charges in Black Hole Thermodynamics
• Extremal vacuum black holes in higher dimensions
• General Nonextremal Rotating Charged AdS Black Holes in Five-dimensional $U(1{)}^3$ Gauged Supergravity: A Simple Construction Method
• Near Horizon Limits of Massless BTZ and Their CFT Duals
• Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM
• EVH Black Holes, AdS3 Throats and EVH/CFT Proposal
• Emergent IR dual 2d CFTs in charged AdS5 black holes
• Extremal Black Holes and First Law of Thermodynamics
• Near-Extremal Vanishing Horizon AdS5 Black Holes and Their CFT Duals
• Nearing 11d Extremal Intersecting Giants and New Decoupled Sectors in D = 3,6 SCFT's
• Warped Ricci-flat reductions
• Dual 2d CFT Identification of Extremal Black Rings from Holes
• EVH Black Hole Solutions With Higher Derivative Corrections
• Emergent AdS_3 in the Zero Entropy Extremal Black Holes
• More on Five Dimensional EVH Black Rings

Cited by in corpus (6)

• Supersymmetric $Ad{S}_5$ black holes and strings from 5D $N=4$ gauged supergravity
• Near Horizon Structure of Extremal Vanishing Horizon Black Holes
• Extremal Vanishing Horizon Kerr-AdS Black Holes at Ultraspinning Limit
• AdS${}_3$ to dS${}_3$ transition in the near horizon of asymptotically de Sitter solutions
• Black Rings in U(1)^3 Supergravity and their dual 2d CFT
• Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity