自耦合克莱因-戈登方程与薛定谔方程的引力孤子解
Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations
AI总结：
本文通过弯曲时空中的克莱因-戈登方程构造薛定谔-牛顿问题的相对论类比，自洽求解场方程得到具有径向激发态的引力孤子解，并与非相对论结果对比。
摘要：
我们利用弯曲时空中的克莱因-戈登方程构造薛定谔-牛顿问题的相对论类比，其中标量粒子处于由其自身概率分布产生的引力势阱中。静态球对称度规由广义相对论场方程计算得出，既直接求解，也通过采用Tolman-Oppenheimer-Volkov流体静力学平衡方程对质量密度建模的完美流体假设来求解。后者适用于玻色星多体问题的Hartree近似。在该弯曲时空中对克莱因-戈登方程进行同步自洽求解，得到具有一系列径向激发态的孤子。我们将结果与非相对论情形进行了比较。
英文摘要：
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.
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