Kerr-CFT and gravitational perturbations
Oscar J.C. Dias, Harvey S. Reall, Jorge E. Santos
TL;DR
This paper studies perturbations of the near-horizon extreme Kerr spacetime, solving the Teukolsky equation, finding no unstable modes, and analyzing energy and angular momentum of the modes.
Contribution
It provides explicit solutions for gravitational perturbations in Kerr spacetime and compares them with Kerr-CFT boundary conditions, advancing understanding of stability.
Findings
No unstable modes found under outgoing boundary conditions
Explicit metric perturbation solutions obtained using Hertz potential
Energy of modes is positive in all cases
Abstract
Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.
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