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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.
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.
The frozen star is a nonsingular, ultracompact object that, to an external observer, looks exactly like a Schwarzschild black hole, but with a different interior geometry and matter composition. The frozen star needs to be sourced by an extremely anisotropic fluid, for which the sum of the radial pressure and energy density is either vanishing or perturbatively small. Here, we show that this matter can be identified with the string fluid resulting from the decay of an unstable D-brane or a brane-antibrane system at the end of open-string tachyon condensation. The string fluid corresponds to flux tubes emanating from the center and ending at the Schwarzschild radius of the star. The effective Lagrangian for this fluid can be recast into a Born-Infeld form. When the fluid Lagrangian is coupled to that of Einstein’s gravity, the static, spherically symmetric solutions of the equations of motion are shown to be the same as those describing the frozen star model. Frozen stars can therefore be viewed as a gravitationally backreacted BIons model or that of gravitationally confined flux tubes. The Born-Infeld Lagrangian provides a complete set of equations that describe the dynamics of the frozen star in a generic state, which is not necessarily static nor spherically symmetric. Our framework therefore should allow a fully dynamical and out-of-equilibrium description of the frozen star model which will be relevant to gravitational waves observations of mergers of astrophysical black holes. Published by the American Physical Society 2024
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