Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited (i.e. nodeful) boson star models. We consider a model including quartic self-interactions, controlled by a coupling Λ. Performing non-linear simulations of the Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson stars solutions of that system, we assess the impact of Λ in the stability properties of the boson stars. In the absence of self-interactions (Λ = 0), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about t ∼104). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning boson stars.

Horndeski fermion-boson stars

We establish the existence of static and spherically symmetric fermion-boson stars, in a low energy effective model of (beyond) Horndeski theories. These stars are in equilibrium, and are composed by a mixing of scalar and fermionic matters that only interact gravitationally one with each other. Properties such as mass, radius, and compactness are studied, highlighting the existence of two families of configurations defined by the parameter c4. These families have distinctive properties, although in certain limits both are reduced to their counterparts in General Relativity. Finally, by assuming the same conditions used in General Relativity, we find the maximum compactness of these hybrid stars and determine that it remains below the so-called Buchdahl's limit.

Ground States for Mass Critical Two Coupled Semi-Relativistic Hartree Equations with Attractive Interactions

We prove the existence and nonexistence of $L^{2}(\mathbb R^3)$-normalized solutions of two coupled semi-relativistic Hartree equations, which arisen from the studies of boson stars and multi-component Bose–Einstein condensates. Under certain condition on the strength of intra-specie and inter-specie interactions, by proving some delicate energy estimates, we give a precise description on the concentration behavior of ground state solutions of the system. Furthermore, an optimal blowing up rate for the ground state solutions of the system is also proved.

Solitary waves and excited states for Boson stars

We study the nonlinear, nonlocal, time-dependent partial differential equation [Formula: see text] which is known to describe the dynamics of quasi-relativistic boson stars in the mean-field limit. For positive mass parameter [Formula: see text] we establish existence of infinitely many (corresponding to distinct energies [Formula: see text]) traveling solitary waves, [Formula: see text], with speed [Formula: see text], where [Formula: see text] corresponds to the speed of light in our choice of units. These traveling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with [Formula: see text]) because Lorentz covariance fails. Instead, we study a suitable variational problem for which the functions [Formula: see text] arise as solutions (called boosted excited states) to a Choquard-type equation in [Formula: see text], where the negative Laplacian is replaced by the pseudo-differential operator [Formula: see text] and an additional term [Formula: see text] enters. Moreover, we give a new proof for existence of boosted ground states. The results are based on perturbation methods in critical point theory.