We consider stationary axisymmetric solutions of general relativity that asymptote to five-dimensional Minkowski space. It is known that this system has a hidden SL(3, R) symmetry. We identify an SO(2, 1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers–Perry black hole starting from the Schwarzschild solution in five dimensions.
Stationary axisymmetric solutions of five dimensional gravity,
GIUSTO, STEFANO;
2007-01-01
Abstract
We consider stationary axisymmetric solutions of general relativity that asymptote to five-dimensional Minkowski space. It is known that this system has a hidden SL(3, R) symmetry. We identify an SO(2, 1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers–Perry black hole starting from the Schwarzschild solution in five dimensions.
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