Gravitational vacuum condensate stars

<jats:p> A new final state of gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate <jats:italic> p <jats:sub>v</jats:sub> </jats:italic> = -ρ <jats:italic> <jats:sub>v</jats:sub> </jats:italic> and an exterior Schwarzschild geometry of arbitrary total mass <jats:italic>M</jats:italic> is constructed. These regions are separated by a shell with a small but finite proper thickness ℓ of fluid with equation of state <jats:italic>p</jats:italic> = +ρ <jats:italic>,</jats:italic> replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order <jats:italic>k</jats:italic> <jats:sub>B</jats:sub> ℓ <jats:italic>Mc</jats:italic> / <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hbar.gif" /> , instead of the Bekenstein–Hawking entropy formula, <jats:italic>S</jats:italic> <jats:sub>BH</jats:sub> = <jats:italic>4</jats:italic> π <jats:italic>k</jats:italic> <jats:sub>B</jats:sub> <jats:italic> GM <jats:sup>2</jats:sup> </jats:italic> / <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hbar.gif" /> <jats:italic>c</jats:italic> . Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox. </jats:p>