Black strings

Black strings
Name	Black strings
Caption	Schematic of a higher-dimensional black string
Field	General relativity
First proposed	Kaluza–Klein theory
Key figures	H. Reall, Robert Emparan, Horowitz, Gregory–Laflamme, R. C. Myers
Notable works	Black hole uniqueness theorem, Myers–Perry metric, Kaluza–Klein black holes

Black strings are extended gravitational solutions in higher-dimensional General relativity that generalize black hole horizons into one or more translationally symmetric directions. They appear in contexts that include Kaluza–Klein theory, string theory compactifications, and higher-dimensional studies such as those involving Anti-de Sitter space, Randall–Sundrum model, and Brane world scenarios. Black strings connect research threads spanning the Myers–Perry metric, the Gregory–Laflamme instability, and holographic correspondences like AdS/CFT correspondence.

Introduction

Black strings were first studied in settings influenced by Kaluza–Klein theory and the search for higher-dimensional analogues of the Schwarzschild metric and Reissner–Nordström metric. Their early analysis involved comparisons with the Schwarzschild–Tangherlini metric and inspired work by Gregory–Laflamme on dynamical stability. Subsequent developments tied black strings to constructions in Type IIB string theory, M-theory, and compactification schemes explored by T. Kaluza and O. Klein.

Theoretical Background

The theoretical basis for black strings rests on higher-dimensional solutions to the Einstein field equations employed in frameworks like Kaluza–Klein theory, Supergravity, and String theory. Studies often reference the Schwarzschild metric, the Myers–Perry metric, and metrics on product manifolds such as Scherk–Schwarz compactification or cylindrical extensions analogous to the Black brane family. Techniques from the analysis of the Einstein–Hilbert action, perturbation theory used by Regge–Wheeler and concepts from the Bekenstein–Hawking entropy program inform construction and interpretation. Work by Gregory–Laflamme, Emparan–Reall, and H. Reall provides rigorous foundations for linear perturbations and non-linear evolutions.

Solutions and Metrics

Explicit black-string solutions include translationally invariant extensions of the Schwarzschild–Tangherlini metric along compact or noncompact directions, often written as direct products with circles like S^1 or with manifolds studied in Calabi–Yau compactifications. Charged and rotating generalizations relate to the Reissner–Nordström metric, Kerr metric, and the Myers–Perry metric, while charged brane solutions draw on results from Type IIB string theory and M-theory p-brane catalogs. Solution-generating techniques involve dualities from T-duality, boosts in compact directions as used in Boosted black strings constructions, and dimensional reduction methods cross-referenced with Kaluza–Klein monopole analysis.

Stability and Gregory–Laflamme Instability

A central result is the Gregory–Laflamme linear instability, demonstrated for uniform black strings by Gregory–Laflamme and elaborated in numerical work by groups including Hubeny, Gubser, and Choptuik. The instability threshold depends on parameters related to the compactification length scales appearing in Kaluza–Klein theory and on thermodynamic comparisons analogous to the Hawking–Page phase transition studied in Anti-de Sitter space. Nonlinear evolution studies by Lehner and Pretorius show horizon fragmentation and relate to cosmic censorship conjectures considered by Roger Penrose and analytic work by H. Reall.

Physical Properties and Thermodynamics

Thermodynamic characterization of black strings borrows from the Bekenstein–Hawking entropy relation and comparisons with localized Kaluza–Klein black holes and black branes; seminal contributions include entropy comparisons by Gubser and phase diagrams developed by Harmark and Obers. Temperature, entropy, and specific heat behaviors are influenced by compactification scales familiar from Randall–Sundrum model contexts and by conserved charges studied in Reissner–Nordström and Myers–Perry families. Connections to the AdS/CFT correspondence enable dual descriptions via thermal states in conformal field theories such as those considered by Juan Maldacena and Edward Witten.

Higher-dimensional Generalizations

Generalizations extend to nonuniform black strings, higher co-dimension configurations, and multi-wrapped objects related to p-branes in String theory and M-theory. Work on localized black holes on cylinders and nonuniform phases is linked to analyses by Kol, Sorkin, and Hollands. The landscape of solutions encompasses charged black strings in Type IIB string theory, spinning analogues connected to Myers–Perry metric families, and constructions using Kaluza–Klein monopole backgrounds or Taub–NUT type fibrations.

Applications and Implications for Physics

Black strings illuminate aspects of dimensionality in gravity, constraints on compactification scenarios relevant to Kaluza–Klein theory and Randall–Sundrum model, and tests of conjectures like cosmic censorship discussed by Roger Penrose. They serve as laboratories for holography in the spirit of AdS/CFT correspondence and for the study of phase transitions akin to the Hawking–Page phase transition. Numerical and analytic progress has influenced research programs at institutions such as CERN and collaborations in numerical relativity centered in groups led by researchers like Matthew Choptuik and Luis Lehner. Ongoing investigations link black-string dynamics to topics addressed in Supergravity, Type IIB string theory, and higher-dimensional phenomenology explored by Edward Witten and Nima Arkani-Hamed.

Category:Higher-dimensional gravity