Perturbations of higher-dimensional spacetimes

Details Perturbations of higher-dimensional spacetimes Perturbations of higher-dimensional spacetimes

2010-08-31

arxiv.org/abs/1009.0015v2

Class.Quant.Grav.28:035011,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages (v2:Minor corrections, accepted by CQG.)

Scientific paper

10.1088/0264-9381/28/3/035011

We discuss linearized gravitational perturbations of higher dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher dimensional generalizations of the 4d Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.

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