Kerr black hole mimickers sourced by a string fluid

We present rotating solutions of Einstein's gravity coupled to an effective Born-Infeld theory that describes the end of open-string tachyon condensation after the decay of an unstable D-brane or a brane-antibrane system. The geometry of these solutions is that of the rotating frozen star. The solutions are stationary, ultracompact, can be made non-singular via a regularization procedure and their exterior geometry is identical, for all practical purposes, to that of the Kerr solution. The Born-Infeld matter consists of radial electric-flux tubes that emanate from, or end at, the ellipsoidal core of the star. Each end of the flux tubes carries an electric charge, so that the electric field can be viewed as being sourced by an ellipsoidal charge distribution of positive and negative charges near the center of the star. Meanwhile, the star's outer layer is equal and oppositely charged, resulting in a vanishing electric field in the external spacetime. We show that these rotating solutions are ultrastable against radial perturbations, just like their static frozen star counterparts. They are also effectively immune to ergoregion instabilities, as we discuss.