TOPICAL REVIEW: General relativistic boson stars

TL;DR

<3-5 sentence high-level summary>General relativistic boson stars are self-gravitating Bose–Einstein condensates described by coupled Einstein–Klein–Gordon dynamics, encompassing complex- and real-scalar fields, self-interactions, charges, and rotation, with extensions to scalar-tensor theories such as Jordan–Brans–Dicke that can introduce gravitational memory effects. The review consolidates the theoretical landscape—Kaup limits, critical masses, rotating branches, and multi-layer anisotropic stress—alongside formation pathways and a broad array of potential observational signatures, including rotation curves, redshift, lensing, microlensing (MACHOs), gravitational waves, and halo phenomenology. It further elaborates on special BS subclasses (BS halos, axidilatons, dilaton/axion stars, soliton-black-hole configurations, and boson–fermion hybrids) and discusses detection strategies across electromagnetic, gravitational, and cosmological channels. The work highlights the interplay between particle physics (scalar fields, self-interactions, and charges) and astrophysical implications (DM halos, galactic centers, and gravitational-wave sources), underlining the potential of BSs to illuminate both fundamental physics and cosmology.

Abstract

There is accumulating evidence that (fundamental) scalar fields may exist in Nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. Similarly as for white dwarfs and neutron stars, there exists a limiting mass, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and the spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation, however, modifications of general relativity, as in the case of Jordan-Brans-Dicke theory as a low energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to constituent mass, an effective radius, and a large particle number. Due to the Heisenberg principle, there exists a completely stable branch, and as a coherent state, it allows for rotating solutions with quantised angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: Possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

Figures (3)

• Figure 1: Feynman graph for the $\lambda |\Phi|^4$ self-interaction in Minkowski spacetime [left]. Feynman graphs for the $e A^\mu \Phi^\ast \partial_\mu \Phi$ (or $e A^\mu \Phi \partial_\mu \Phi^\ast$, resp.) [middle] and for the $e^2 A_\mu A^\mu |\Phi|^2$ [right] self-interaction.
• Figure 2: Reduced deflection angle for a mini-BS of critical mass. The angle $\vartheta$ for the image positions is given in units of arcsec times the distance function $n$DS00.
• Figure 3: Left: Mass $M$ and particle number $N$ (or rest mass $mN$ at infinity) of a mini-BS depending on the central density $\rho$. Right: Mass-radius dependence of a mini-BS.