Self-gravitating Bose-Einstein Condensates

Abstract

Bose-Einstein condensates play a major role in condensed matter physics. Recently, it has been suggested that they could play an important role in astrophysics also. Indeed, dark matter halos could be gigantic quantum objects made of Bose-Einstein condensates. The pressure arising from the Heisenberg uncertainty principle or from the repulsive scattering of the bosons could stabilize dark matter halos against gravitational collapse and lead to smooth core densities instead of cuspy density profiles in agreement with observations. In order to reproduce the scales of dark matter halos, the mass of the bosons may range from \(10^{-24}\, \mathrm{eV/c^2}\) to a few \(\mathrm{eV/c^2}\) depending whether they interact or not. At the scale of galaxies, Newtonian gravity can be used so the evolution of the wave function is governed by the Gross-Pitaevskii-Poisson system. Self-gravitating Bose-Einstein condensates have also been proposed to describe boson stars. For these compact objects, one must use general relativity and couple the Klein-Gordon equation to the Einstein field equations. In that context, it has been proposed that neutron stars could be Bose-Einstein condensate stars due to their superfluid core. Indeed, the neutrons could form Cooper pairs and behave as bosons. In that case, the maximum mass of the neutron stars depends on the scattering length of the bosons and can be as large as \(2M_{\odot }\). This could explain recent observations of neutron stars with a mass much larger than the Oppenheimer-Volkoff limit of \(0.7M_{\odot }\) obtained by assuming that neutron stars are ideal fermion stars. Self-gravitating Bose-Einstein condensates may also find applications in the physics of black holes. For example, when the scattering length of the bosons is negative, a Newtonian self-gravitating Bose-Einstein condensate becomes unstable above a critical mass and undergoes a gravitational collapse leading ultimately to a singularity. On the other hand, stable boson stars with a positive scattering length could mimic supermassive black holes that reside at the center of galaxies. Finally, it has been proposed that microscopic quantum black holes could be Bose-Einstein condensates of gravitons. This contribution discusses fundamental aspects of the physics of self-gravitating Bose-Einstein condensates and considers recent applications in astrophysics, cosmology and black hole physics with promising perspectives.