# Non-singular space-times with a negative cosmological constant: V. Boson stars

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## Abstract

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.

## Keywords

Boson stars Negative cosmological constant Periodic solutions of Einstein equations## Mathematics Subject Classification

83C20 83E15## Notes

### Acknowledgements

The research of PTC was supported in part by the Austrian Research Fund (FWF), Project P29517-N27, by the Polish National Center of Science (NCN) under Grant 2016/21/B/ST1/00940 and by the Erwin Schrödinger Institute. Armin Rainer was supported by the FWF-Project P 26735-N25. Paul Klinger was supported by a uni:docs grant of the University of Vienna. We are grateful to Gilles Carron and Luc Nguyen for useful comments and discussions.

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