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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/144265
The Gross-Pitaevskii equations of a static and spherically symmetric condensate of gravitons
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In this paper we consider the Dvali and Gómez assumption that the end state of a gravitational collapse is a Bose-Einstein condensate of gravitons. We then construct the two Gross-Pitaevskii equations for a static and spherically symmetric configuration of the condensate. These two equations correspond to the constrained minimisation of the gravitational Hamiltonian with respect to the redshift and the Newtonian potential, per given number of gravitons. We find that the effective geometry of the condensate is the one of a gravastar (a de Sitter star) with a sub-Planckian cosmological constant, for masses larger than the Planck scale. Thus, a condensate corresponding to a semiclassical black hole, is always quantum and weakly coupled. Finally, we obtain that the boundary of our gravastar, although it is not the location of a horizon, corresponds to the Schwarzschild radius.
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CUNILLERA GARCÍA, Francesc and GERMANI, Cristiano. The Gross-Pitaevskii equations of a static and spherically symmetric condensate of gravitons. Classical and Quantum Gravity. 2018. Vol. 35, num. 10, pags. 105006. ISSN 0264-9381. [consulted: 10 of August of 2026]. Available at: https://hdl.handle.net/2445/144265