The self–gravitating Bose–Einstein condensate Kingsley R W Jones† and David Bernstein‡ † County Investment Management, GPO Box 231 E, Melbourne 3001, Australia. ‡ Tanner Research, 2650 E. Foothill Blvd., Pasadena, CA 91107, USA. Abstract. We study the characteristics of Bose–Einstein condensates formed by the action of three different potentials: Newtonian self-gravity, hard-sphere repulsion (the Gross–Pittaevski potential), and a harmonic trap potential as used in laboratory experiments. We show that in a certain regime a condensate can form which is much larger than predicted by the quantum self-gravitational ground state radius. Furthermore, the size is independent of the number of particles in the condensate. We speculate that massive objects of this type may form in extreme isolation through gravitational accretion onto a fixed size object. We propose that these be called Deep Space Quantum Objects, or DSQOs (discos). Analytical Hartree–Fock solutions for the DSQO ground state are obtained, along with a formula for the limiting DSQO radius and energy. These are then compared with numerical simulations. Prospects for DSQO formation are briefly discussed with emphasis on possible cooling mechanisms and the dynamic stability of structures formed by accretion. PACS numbers: 03.65, 03.75 and 95.35 Submitted to: Class. Quantum Grav. 1. Introduction Whereas the province of quantum gravitational effects is customarily thought of as Planck scale physics, there is another avenue to increase the threshold of detection for gravitational effects using emergent collective properties of quantum many–body systems. As pointed out by Jones[1], the mutual gravitational attraction between bodies does not screen, so that higher energy scales can be accessed by accumulating many stationary particles in one place. Thus we can imagine taking many cold and massive quantum particles to amplify the effects of quantum gravitation to detectable levels. This observation leads us to examine the low energy limit of nonrelativistic, or Newtonian quantum gravity [1, 2, 3, 4, 5, 6, 7, 8, 9], and to focus on possible signatures of gravitation in many–body physics. Of particular interest is the suggestion by Penrose[4] that gravity may not respect the superposition principle. † kingsley jones@county.com.au ‡ dhbernstein@earthlink.net