Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations

Abstract

We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schrödinger-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.

arXiv comment15 pages, 5 figures, RevTex 4.2; added new calculation based directly on GR equations and corrected error in original work

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Cited by in corpus (1)

• Techniques for Solving Static Klein-Gordon Equation with Self-Interaction $\lambda {\varphi }^4$ and Arbitrary Spherical Source Terms