Stability analysis of self-gravitating skyrmions

Details Stability analysis of self-gravitating skyrmions Stability analysis of self-gravitating skyrmions

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phlb..271...61h&link_type=abstract

Physics Letters B, Volume 271, Issue 1-2, p. 61-67.

Physics

50

Scientific paper

We investigate the stability of our recently constructed self-gravitating skyrmions in the framework of small time-dependent perturbations. It is shown that the frequency spectrum for radial perturbations of the coupled Einstein-Skyrme equations can be reduced to the energy spectrum of a p-wave Schrödinger equation with a bounded effective potential, which is determined by the equilibrium solution. Bound states of this Schrödinger equation correspond to exponentially growing modes. It turns out that there are no such modes, as long as the relevant dimensionless coupling constant (κ) is less than a critical value, κc. For larger values of κ there is exactly one unstable mode. Therefore, the Skyrme ``stars'' become unstable (in the sense of Liapunov) for κ>κc, in spite of the fact that their topological winding number is conserved. The linear stability for κ<κc (with respect to radial modes) is, of course, only a necessary condition for (non-linear) stability. Similar results are expected to hold for our new black hole solutions of the Einstein-Skyrme system.

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