On the Equilibrium State of a Gravitating Bose–Einstein Condensate

• Published in: Journal of experimental and theoretical physics Vol. 127; no. 5; pp. 889 - 902
• Main Author: Meierovich, B. E.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.11.2018; Springer; Springer Nature B.V
• Subjects: Absolute zero; BLACK HOLES; Bose-Einstein condensates; BOSE-EINSTEIN CONDENSATION; BOSONS; Classical and Quantum Gravitation; COMPARATIVE EVALUATIONS; Condensates; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CRITICAL MASS; DENSITY; Elementary Particles; Energy levels; ENERGY SPECTRA; EQUILIBRIUM; Fermions; Galaxies; GALAXY NUCLEI; Gravitation; GRAVITATIONAL FIELDS; Ground state; GROUND STATES; Laboratories; Particle and Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theory; Relativity Theory; SCALAR FIELDS; Solid State Physics; WAVE FUNCTIONS
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776118110158

The properties of a scalar field in equilibrium with its own gravitational field are discussed. The scalar field serves as the wavefunction of a Bose–Einstein condensate in equilibrium at a temperature close to absolute zero. The wavefunction of a laboratory Bose–Einstein condensate satisfies the Gross–Pitaevskii equation. The superheavy objects (most likely black holes) at the centers of galaxies are the subject of applying the theory of gravitating fermion and boson clusters. In contrast to a laboratory experiment, the energy spectrum of gravitating bosons is a functional of the wavefunction for the entire condensate. The very presence of a level depends on its population. In particular, at zero temperature for each level, there is a critical total mass M cr above which an equilibrium configuration (and, hence, this level) does not exist. The critical mass M cr increases proportionally to the level number. At M > M cr , the next level acts as the ground state. The concept of the ground state of a boson system is modified. The radius of the sphere occupied by the condensate also increases proportionally to the level number and, therefore, the density does not grow with increasing condensate mass; as long as the spacing between nearby energy levels is great compared to the temperature, no constraints on the total mass arise. One bunch of bosons at a high quantum level with a large mass is energetically less favorable than several isolated centers, with a condensate at the zeroth quantum level being in each of them.