Stationary and axisymmetric solutions of higher-dimensional general relativity
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Stationary and axisymmetric solutions of higher-dimensional general relativity. / Harmark, Troels.
I: Physical Review D, Bind 70, Nr. 12, 124002, 01.01.2004.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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