One can consider a perfect fluid as the fermionic component such that the stress-energy tensor takes the standard form
whereThe perfect fluid obeys relativistic versions of the Euler equations, which account for the conservation of the fluid energy and momentum, plus the conservation of the baryonic number (i.e., mass conservation). The complex scalar field representing the bosonic component is once again described by the Klein–Gordon equation. The spacetime is computed through the Einstein equations with a stress-energy tensor, which is a combination of the complex scalar field and the perfect fluid
After imposing the harmonic time dependence of Eq. (33These equations can be written in adimensional form by rescaling the variables by introducing the following quantities
By varying the central value of the fermion densityIt was shown that the stability arguments made with boson stars can also be applied to these mixed objects [121]. The existence of slowly rotating fermion-boson stars was shown in [65], although no solutions were found in previous attempts [136]. Also see [73] for unstable solutions consisting of a real scalar field coupled to a perfect fluid with a polytropic equation of state.
http://www.livingreviews.org/lrr-2012-6 |
Living Rev. Relativity 15, (2012), 6
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