Black holes on cylinders are not algebraically special

Abstract

We give a Petrov classification for five-dimensional metrics. We classify Ricci-flat metrics that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to look for the metric of a black hole on a cylinder, i.e. a black hole with asymptotic geometry four-dimensional Minkowski space times a circle. Although a black string wrapped around the circle and the five-dimensional black hole are both algebraically special, it turns out that the black hole on a cylinder is not.

21 pages, 1 figure; v2: classification completed, discussion simplified, references added

References in corpus (7)

• A rotating black ring in five dimensions
• Generalized Weyl Solutions
• On non-uniform black branes
• Fate of the Black String Instability
• Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions
• Black Holes on Cylinders
• Playing with Black Strings

Cited by in corpus (51)

• Black Holes in Higher Dimensions
• Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
• Higher dimensional black holes and supersymmetry
• Particle and light motion in a space-time of a five-dimensional rotating black hole
• The Phase Transition between Caged Black Holes and Black Strings - A Review
• Instabilities of Black Strings and Branes
• A critical dimension in the black-string phase transition
• Topology change in General Relativity and the black-hole black-string transition
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Small Black Holes on Cylinders
• New Phase Diagram for Black Holes and Strings on Cylinders
• A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
• Phase Structure of Black Holes and Strings on Cylinders
• Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
• Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
• Evidence that highly non-uniform black strings have a conical waist
• Weyl doubling
• Black Holes in Higher-Dimensional Gravity
• Phases of Kaluza-Klein Black Holes: A Brief Review
• Higher dimensional bivectors and classification of the Weyl operator
• The Kerr-Newman-Godel Black Hole
• On a five-dimensional version of the Goldberg-Sachs theorem
• The Kerr-Newman metric: A Review
• Classification of Higher Dimensional Spacetimes
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Spinor classification of the Weyl tensor in five dimensions
• On the geometry of Killing and conformal tensors
• Distorted 5-dimensional vacuum black hole
• Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1
• Asymptotic structure of radiation in higher dimensions
• Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D
• The Petrov type of the five-dimensional Myers-Perry metric
• Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
• Refinements of the Weyl tensor classification in five dimensions
• Algebraically special perturbations of the Schwarzschild solution in higher dimensions
• Spinor description of $D=5$ massless low-spin gauge fields
• Coordinate independent approach to 5d black holes
• Algebraic classification of five-dimensional spacetimes using scalar invariants
• Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1
• The Petrov type of the BMPV metric
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• Spinors and the Weyl Tensor Classification in Six Dimensions
• Black Holes and Black Strings on Cylinders
• Five-dimensional metrics of Petrov type 22
• Spinor calculus on 5-dimensional spacetimes
• Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
• On stationary metrics in five dimensions
• Conformally Invariant Spinorial Equations in Six Dimensions
• Killing Spinors and Related Symmetries in Six Dimensions
• On the Pursuit of Generalizations for the Petrov Classification and the Goldberg-Sachs Theorem