General relativistic rotating boson stars were later found [193, 222] with the same ansatz of Eq. (67). To obtain stationary axially symmetric solutions, two symmetries were imposed on the spacetime described by two commuting Killing vector fields and in a system of adapted (cylindrical) coordinates . In these coordinates, the metric is independent of and and can be expressed in isotropic coordinates in the Lewis–Papapetrou form
The entire family of solutions for and part of was computed using the self-consistent field method , obtaining a maximum mass . Both families were completely computed in  using faster multigrid methods, although there were significant discrepancies in the maximum mass, which indicates a problem with the regularity condition on the z-axis. The mass and angular momentum for stationary asymptotically flat spacetimes can be obtained from their respective Komar expressions. They can be read off from the asymptotic expansion of the metric functions and  discussed in Section 6.3. Figure 7 shows the scalar field for two different rotating BSs.
Recently, their stability properties were found to be similar to nonrotating stars . Rotating boson stars have been shown to develop a strong ergoregion instability when rapidly spinning on short characteristic timescales (i.e., 0.1 seconds – 1 week for objects with mass and angular momentum ), indicating that very compact objects with large rotation are probably black holes .
More discussion concerning the numerical methods and limitations of some of these approaches can be found in Lai’s PhD thesis .
Living Rev. Relativity 15, (2012), 6
This work is licensed under a Creative Commons License.