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arXiv · 2212.14166

Gravitational soliton solutions to self-coupled Klein-Gordon and Schr\"odinger equations

D. A. Taylor·S. S. Chabysheva·J. R. Hiller
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Abstract

We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schr\"odinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution. A static, spherically symmetric metric is computed from the field equations of general relativity, both directly and as modeled by a perfect-fluid assumption that uses the Tolman-Oppenheimer-Volkov equation for hydrostatic equilibrium of the mass density. The latter is appropriate for a Hartree approximation to the many-body problem of a bosonic star. Simultaneous self-consistent solution of the Klein--Gordon equation in this curved spacetime then yields solitons with a range of radial excitations. We compare results with the nonrelativistic case.

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D. A. Taylor, S. S. Chabysheva, J. R. Hiller. 2022-12-29. Gravitational soliton solutions to self-coupled Klein-Gordon and Schr\"odinger equations. https://doi.org/10.1103/physrevd.107.124049

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