Although bosons in the same state are indistinguishable, it is possible to construct non-trivial
configurations with bosons in different excited states. A system of bosons in different states that only
interact with each other gravitationally can be described by the following Lagrangian density
In the simplest case of a multi-state boson, one has the ground state and the first excited state. Such configurations are stable if the number of particles in the ground state is larger than the number of particles in the excited state [25, 7]
This result can be understood as the ground state deepens the gravitational potential of the excited state, and thereby stabilizing it. Unstable configurations migrate to a stable one via a flip-flop of the modes; the excited state decays, while the ground jumps to the first exited state, so that the condition (78 Similar results were found in the Newtonian limit [215], however, with a slightly higher stability
limit . This work stresses that combining several excited states makes it
possible to obtain flatter rotation curves than only with ground state, producing better models for
galactic dark matter halos (see also discussion of boson stars as an explanation of dark matter in
Section 5.3).
Ref. [110] considers two scalar fields describing boson stars that are phase shifted in time with respect
to each other, studying the dynamics numerically. In particular, one can consider multiple scalar fields with
an explicit interaction (beyond just gravity) between them, say . Refs. [37, 38] construct
such solutions, considering the individual particle-like configurations for each complex field as interacting
with each other.
http://www.livingreviews.org/lrr-2012-6 |
Living Rev. Relativity 15, (2012), 6
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