Stationary and axisymmetric solutions of higher-dimensional general relativity
Top Cited Papers
- 3 December 2004
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 70 (12) , 124002
- https://doi.org/10.1103/physrevd.70.124002
Abstract
We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. -dimensional stationary and axisymmetric solutions are defined as having 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 by matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a by 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.
Keywords
All Related Versions
This publication has 21 references indexed in Scilit:
- Phases of Kaluza–Klein black holesClassical and Quantum Gravity, 2004
- A charged rotating black ringPhysical Review D, 2003
- Axisymmetric metrics in arbitrary dimensionsClassical and Quantum Gravity, 2003
- A new form of the C-metricClassical and Quantum Gravity, 2003
- Generalized Weyl solutionsPhysical Review D, 2002
- A Rotating Black Ring Solution in Five DimensionsPhysical Review Letters, 2002
- Black holes in general relativityCommunications in Mathematical Physics, 1972
- Topology of Some Spheroidal MetricsJournal of Mathematical Physics, 1966
- Eine rotationssymmetrische Lösung in der allgemeinen RelativitätstheorieAnnalen der Physik, 1953
- Zur GravitationstheorieAnnalen der Physik, 1917