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arXiv · 1708.05674

Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions

Carlos A. R. Herdeiro·Alexandre M. Pombo·Eugen Radu
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Abstract

The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field -- $geons$ -- was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar) boson stars. Similar geons have subsequently been found in Einstein-Dirac theory and, more recently, in Einstein-Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin $0,1/2$ and $1$, emphasising the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermonic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.

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Carlos A. R. Herdeiro, Alexandre M. Pombo, Eugen Radu. 2017-08-18. Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions. https://doi.org/10.1016/j.physletb.2017.09.036

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