Stationary and axisymmetric solutions of higher-dimensional general relativity

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Stationary and axisymmetric solutions of higher-dimensional general relativity. / Harmark, Troels.

In: Physical Review D, Vol. 70, No. 12, 124002, 01.01.2004.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Harmark, T 2004, 'Stationary and axisymmetric solutions of higher-dimensional general relativity', Physical Review D, vol. 70, no. 12, 124002. https://doi.org/10.1103/PhysRevD.70.124002

APA

Harmark, T. (2004). Stationary and axisymmetric solutions of higher-dimensional general relativity. Physical Review D, 70(12), [124002]. https://doi.org/10.1103/PhysRevD.70.124002

Vancouver

Harmark T. Stationary and axisymmetric solutions of higher-dimensional general relativity. Physical Review D. 2004 Jan 1;70(12). 124002. https://doi.org/10.1103/PhysRevD.70.124002

Author

Harmark, Troels. / Stationary and axisymmetric solutions of higher-dimensional general relativity. In: Physical Review D. 2004 ; Vol. 70, No. 12.

Bibtex

@article{12eccfe624af4f8697f596fc4d0acd0d,
title = "Stationary and axisymmetric solutions of higher-dimensional general relativity",
abstract = "We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. [Formula Presented]-dimensional stationary and axisymmetric solutions are defined as having [Formula Presented] commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric [Formula Presented] by [Formula Presented] matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a [Formula Presented] by [Formula Presented] matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.",
author = "Troels Harmark",
year = "2004",
month = jan,
day = "1",
doi = "10.1103/PhysRevD.70.124002",
language = "English",
volume = "70",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Physical Society",
number = "12",

}

RIS

TY - JOUR

T1 - Stationary and axisymmetric solutions of higher-dimensional general relativity

AU - Harmark, Troels

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. [Formula Presented]-dimensional stationary and axisymmetric solutions are defined as having [Formula Presented] commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric [Formula Presented] by [Formula Presented] matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a [Formula Presented] by [Formula Presented] matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.

AB - We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. [Formula Presented]-dimensional stationary and axisymmetric solutions are defined as having [Formula Presented] commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric [Formula Presented] by [Formula Presented] matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a [Formula Presented] by [Formula Presented] matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.

UR - http://www.scopus.com/inward/record.url?scp=85039589728&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.70.124002

DO - 10.1103/PhysRevD.70.124002

M3 - Journal article

AN - SCOPUS:85039589728

VL - 70

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 12

M1 - 124002

ER -

ID: 229999984