Stability of Squashed Kaluza-Klein Black Holes

TL;DR

Stability of squashed Kaluza-Klein black holes investigates linear gravitational stability in five-dimensional KK spacetimes by exploiting the $U(2)$ symmetry of SqKK black holes. The authors construct a Wigner-function based perturbation framework, derive Schrödinger-type master equations for the relevant modes, and demonstrate positive definite effective potentials (via direct analysis and $S$-deformation) for the studied sectors. This yields strong evidence that SqKK black holes are stable within the analyzed perturbation space, supporting their role as realistic KK black holes and suggesting potential observational signatures in Hawking radiation and quasinormal modes. The work also outlines future extensions to rotating SqKK black holes and higher-dimensional generalizations, which could further illuminate extra-dimensional physics.

Abstract

The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.

Figures (4)

• Figure 1: The effective potential $V_2$ for $K=\pm2$ mode.
• Figure 2: The effective potential $V_1$ for $K=\pm1$ mode.
• Figure 3: The effective potential $V_0$ for $K=0$ mode.
• Figure 4: The deformation functions $S$ for various $\rho_0$ with the boundary condition $S|_{\rho = 50 \rho_+ } = 0$.