Extreme ℓ-boson stars

Abstract

A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular momentum, while still maintaining the spacetime's spherical symmetry. These new solutions depend on an (integer) angular parameter $\ell$, and hence were named $\ell$-boson stars. Like the standard $\ell=0$ boson stars these configurations admit a stable branch in the solution space; however, contrary to them they have a morphology that presents a shell-like structure with a "hole" in the internal region. In this article we perform a thorough exploration of the parameter space, concentrating particularly on the extreme cases with large values of $\ell$. We show that the shells grow in size with the angular parameter, doing so linearly for large values, with the size growing faster than the thickness. Their mass also increases with $\ell$, but in such a way that their compactness, while also growing monotonically, converges to a finite value corresponding to about one half of the Buchdahl limit. Furthermore, we show that $\ell$-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large $\ell$, reducing asymptotically to zero, and with the maximum density also approaching zero. We show that these properties can be understood by analyzing the asymptotic limit $\ell\rightarrow\infty$ of the field equations and their solutions. We also analyze the existence and characteristics of both timelike and null circular orbits, especially for very compact solutions.

Rotating boson stars using finite differences and global Newton methods

“…These objects consider an additional harmonic decomposition in the rotation angle ϕ, Φ(r, t) = φ(r) e −i(ωt−lϕ) , (1.4) where l is an integer known as the azimuthal rotation number. As expected, rotating boson stars have non-zero angular momentum and greater complexities than their spherical siblings (notice that this is quite different from the -boson stars recently studied by Alcubierre et al [28], which are particular combinations of several scalar fields that result in spherical objects with non-zero total angular momentum). Rotating boson stars were first studied by Silveira and Sousa in Newtonian theory [29].…”

Total light bending in non-asymptotically flat black hole spacetimes

“…A.1. Technical results for the Kottler solution In section 2.3 we present the result of the surface integral equation (15),…”

“…A similar effect, but in the strong gravity regime (beyond the weak field limit), is the strong lensing effect, which provides an experimental test for compact astrophysical objects, such as black holes, e.g. the one embedded in M87 galaxy [10] and SgrA* [11], or exotic ultracompact objects like boson stars [12,13], ℓ-boson stars [14][15][16][17], Horndeski stars [18,19], or other exotic compact objects such as superspinars, anisotropic stars, etc (see for example table 1 in [20]).…”

Magnetostatic Boson Stars

“…Anisotropic pressures are essential to obtain equilibrium configurations with high compactness and large values for the mass. In [35] (see [38] for recent discussion on fluid anisotropic stars and [39] for shell-type configurations in the Einstein-Vlasov system) it was shown that for ℓ-boson stars, small radial pressures and big tangential pressures are related to an increase in the mass and radius of the star in a way that resembles the forces on an arch. In our case, to understand the decrease in size of the magnetic boson stars, we start by noticing that the tangential pressure is composed by two different contributions, S θ θ and S ϕ ϕ , which act together with the radial pressure (and with the Lorentz force in some region) against gravity in order to support the configuration.…”