$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous study assessed the stability of $\ell$-boson stars under spherical perturbations, finding that there are both stable and unstable branches of solutions, as for single-field boson stars ($\ell=0$). In this work we probe the stability of $\ell$-boson stars against non-spherical perturbations by performing numerical evolutions of the Einstein-Klein-Gordon system, with a 3D code. For the timescales explored, the $\ell$-boson stars belonging to the spherical stable branch do not exhibit measurable growing modes. We find, however, evidence of zero modes; that is, non-spherical perturbations that neither grow nor decay. This suggests the branching off towards a larger family of equilibrium solutions: we conjecture that $\ell$-boson stars are the enhanced isometry point of a larger family of static (and possibly stationary), non-spherical multi-field self-gravitating solitons.
In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number $\ell$. We call such solutions "$\ell$-boson stars". Here, we perform a series of fully non-linear dynamical simulations of perturbed $\ell$-boson stars in order to study their stability, and the final fate of unstable configurations. We show that for each value of $\ell$, the configuration of maximum mass …
Fully non-linear numerical evolutions of the Einstein-(multi)--Klein-Gordon equations are performed to study head-on collisions of $\ell$-boson stars. Despite being spherically symmetric, $\ell$-boson stars have a (hidden) frame of reference, used in defining their individual multipolar fields. To assess the impact of their relative orientation, we perform simulations with different angles between the axes of the two colliding stars. Additionally, two scenarios are considered for the colliding stars: that they are composites of either the same or different scalar fields. Despite some model-spe…
Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol
In previous work we constructed new boson star solutions consisting of a family of massive complex scalar fields minimally coupled to gravity in which the individual fields have angular momentum, yet the configuration as a whole is static and spherically symmetric. In the present article we study the linear stability of these $\ell$-boson stars with respect to time-dependent, radial perturbations. The pulsation equations, governing the dynamics of such perturbations are derived, generalizing previous work initiated by M. Gleiser, and shown to give rise to a two-channel Schrödinger operator. Us…
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 stru…
We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein-Klein-Gordon system for a collection of an arbitrary odd number $N$ of complex scalar fields with an internal $U(N)$ symmetry and no self-interactions. These solutions, which we dub $\ell$-boson stars, are parametrized by an angular momentum number $\ell=(N-1)/2$, an excitation number $n$, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For $\ell = 0$ the standard spherically symmetric boson stars are recovered. …
Mixing of spherical and spheroidal modes in perturbed Kerr black holes
在紧密双星合并和引力坍缩中发射的引力辐射的角度依赖性通常使用自旋加权球谐函数${}_sY_{\ell m}$分离，自旋加权球谐函数$s$在$s=0$时减少到普通球谐函数$Y_{\ell m}$。Teukolsky首先证明了这些事件可能产生的克尔黑洞的扰动可以用一组不同的角函数来分离：自旋加权球谐函数${}_sS_{\ell m n}$，其中$n$表示相应的克尔准正规模频率$ω_{\ell m n}$的“泛音指数”。本文计算了${}_sS_{\ell m n}$与${}_sY_{\ell m}$（“球-球混合系数”）以及与它们自身（“球-球混合系数”）的复值标量积，作为无量纲Kerr参数$j$的函数。这些系数的表格和它们对$j$依赖性的解析拟合可以在网上找到，用于引力波源建模和黑洞微扰理论的其他应用。
In this manuscript the three types of late-time behavior of spherically symmetric Boson Stars are presented, these are: stable configurations, unstable bounded that collapse to form black holes and unstable unbounded that explode. The results are found by solving the spherically symmetric Einstein-Klein-Gordon system of equations for a complex scalar field with initial conditions corresponding to a Boson Star. The solution is based on a constrained evolution that uses the method of lines for the scalar field and solves the constraint equations for the geometry on the fly.
We prove boundedness and polynomial decay statements for solutions to the spin $\pm1$ Teukolsky-type equation projected to the $\ell=1$ spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor. This gives a first description in physical space of gauge-invariant quantities transporting the electromagnetic radiation in perturbations of a charged black hole. The proof is based on the use of derived quantities, introduced in previous works on linear stability of Schwarzsc…
We construct boson star configurations in quantum field theory using the semiclassical gravity approximation. Restricting our attention to the static case, we show that the semiclassical Einstein-Klein-Gordon system for a {\it single real quantum} scalar field whose state describes the excitation of $N$ {\it identical particles}, each one corresponding to a given energy level, can be reduced to the Einstein-Klein-Gordon system for $N$ {\it complex classical} scalar fields. Particular consideration is given to the spherically symmetric static scenario, where energy levels are labeled by quantum…
