Scalar Field as a Bose-Einstein Condensate?

Abstract

We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi--bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surrounding a black hole.

17 pages, 5 figures

References in corpus (5)

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• Schwarzschild scalar wigs: spectral analysis and late time behavior
• Surprising Connections Between General Relativity and Condensed Matter
• Non-relativistic approach for cosmological Scalar Field Dark Matter
• Emergent Horizons in the Laboratory

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