6 Boson Stars in Mathematical Relativity

Although the experimental foundation for the existence of boson stars is completely lacking, on the theoretical and mathematical front, boson stars are well studied. Recent work includes a mathematical approach in terms of large and small data [87], followed up by studying singularity formation [151] and uniqueness [88, 150] for a certain boson star equation. In Ref. [48], they study radial solutions of the semi-relativistic Hartree type equations in terms of global well-posedness. Ref. [30] demonstrates stationarity of time periodic scalar field solutions.

Beyond just existence, however, boson stars are often employed mathematically to study dynamics. Here, we concentrate on a few of these topics that have attracted recent interest.

 6.1 Black hole critical behavior
 6.2 Hoop conjecture
 6.3 Other dimensions

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