Antikink-kink ($\overline{\mathrm{K}}\mathrm{K}$) collisions in the ${\varphi }^6$ model exhibit resonant scattering although the ${\varphi }^6$ kinks do not support any bound states to which energy could be transferred. In P. Dorey et al. [Kink-Antikink Collisions in the ${\varphi }^6$ Model, Phys. Rev. Lett. 107, 091602 (2011)] it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\overline{\mathrm{K}}\mathrm{K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\overline{\mathrm{K}}\mathrm{K}$ scattering based on this collective bound mode trapped between the $\overline{\mathrm{K}}\mathrm{K}$ pair which allows us to reproduce the full dynamics of $\overline{\mathrm{K}}\mathrm{K}$ scattering with striking accuracy. We also study kink-antikink ($\mathrm{K}\overline{\mathrm{K}}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered.

We compute the gravitational form factor $D(t)$ of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number $B$. We separately discuss the cases $B=1$ (nucleons), $B=2$ (deuteron), $B=3$ (helium-3 and tritium), and extrapolate to larger $B$-values. Configurations with $B>1$ are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with $B=1,2,3,4,5,6,7,8$, 32, 108. We find that the $B$-dependence is consistent with a power-law $D(0)\propto B^{\beta }$ with $\beta =1.7–1.8$. Other gravitational form factors can be calculated in the same framework, and we show the result for the $J(t)$ form factor associated with the angular momentum for the $B=3$ solution.

Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future gravitational wave (GW) detectors. In this work we show that the moment of inertia $I$, the (dimensionless) angular momentum $\chi$, and the quadrupole moment $Q$ of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained $I-\chi -Q$ relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e., model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars.

First proposed in 2013 by Yagi and Yunes, the quasiuniversal I-Love-Q relations consist of a set of relations between the moment of inertia, the spin-induced quadrupole moment and the electric quadrupolar tidal deformability of neutron stars which are independent of the equation of state within an accuracy of $\sim 1\%$. In this work, we show that these relations hold for different Skyrme-based nuclear matter equation of state and also for the starlike solutions of different Einstein-BPS-Skyrme models - where BPS stands for Bogomolnyi-Prasad-Sommerfield, some of which do not even present a barotropic equation of state. Further, other quasiuniversal relations are analyzed, and, together with recent gravitational wave observations, we use them to select the generalized Skyrme model that better reproduces observations. Our results reaffirm both the universality of the I-Love-Q relations and the suitability of generalized Skyrme models to describe nuclear matter inside neutron stars.

A general review of the crystalline solutions of the generalized Skyrmemodel and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrmemodel on the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first-order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass–radius curves already reasonably satisfy current astrophysical constraints.