Ergoregion instability revisited - A new and general method for numerical analysis of stability

Abstract

Ergoregion instability of rapidly rotating relativistic stars found by Friedman is investigated numerically by developing a totally different formulation from the one presented by Comins & Schutz. Our new scheme can provide solutions even for modes of small azimuthal number m, which Comins & Schutz could not precisely investigate because of their use of the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation. For several models with stronger gravity and more rapid rotation than those investigated by Comins & Schutz, we have shown that e-folding times for lower modes are sufficiently short compared with the age of the universe. Although the new method is applied here to a one-dimensional problem which is devised to mimic the ergoregion instability in two-dimensional space by Comins & Schutz, there is no obstacle to extending the analysis to the original problems in two dimensions. Moreover our scheme seems suitable for the mode analysis of rapidly rotating and highly deformed systems. Since we have made our formulation as general as possible, we have applied our new method to the analysis of axial modes of the non-rotating ultracompact stars investigated by Chandrasekhar & Ferrari and Kokkotas. Our results agree well with those of both groups.