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In this article we study properties of isospin asymmetric nuclear matter in the generalized Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found multi-wall skyrmion crystal. We obtain, for the first time, an equation of state from the Skyrme model which interpolates between infinite isospin asymmetric nuclear matter and finite isospin symmetric atomic nuclei. This enables us to describe neutron stars with crusts within the Skyrme framework. Furthermore, we observe that the symmetry energy tends to a constant value at zero density, which can be identified with the asymmetry coefficient in the semi-empirical mass formula for atomic nuclei. The symmetry energy also reveals a cusp in its structure below the nuclear saturation point $n_0$ at $n_*\sim 3n_0/4$. This cusp density point $n_*$ can be interpreted as the nuclear density whereby the infinite crystalline multi-wall configuration undergoes a phase transition to a finite isolated multi-wall configuration. Both of these observations are observed to be generic features of skyrmion crystals that tend asymptotically to somewhat isolated skyrmion configurations in the zero density limit. We find that the resulting neutron stars from our study agree quite well with recent NICER/LIGO observational data., Comment: 38 pages, 7 figures

Boson Stars are, at present, hypothetical compact stellar objects whose existence, however, could resolve several enigmas of current astrophysics. If they exist, either as independent astrophysical entities or as a matter admixture of more standard compact stars, then their imprints can probably be observed in the not-too-distant future from the gravitational signal of coalescing binaries in current and future GW detectors. Here we show that the multipole moments of rotating boson stars obey certain universal relations, valid for a broad set of models and various states in terms of the \textit{harmonic indices}. These universal relations are equivalent to a kind of no-hair theorem for this exotic matter, allowing to map these universal (i.e. model independent) multipoles to an equally universal gravitational field around the stellar object. Further, the multipole moments can be related to observable astrophysical quantities., Comment: 17 pages, 21 figures. We have added some references

The Skyrme model is an effective theory for the description of nucleons, nuclei and pions, where the primary degrees of freedom are mesons and the hadrons and nuclei appear as topological solutions of such model. Furthermore, the number of baryons is identified with the topological charge of the solitons. The Skyrme model allow us to study hadrons and nuclei starting from a field theory instead of the more common nuclear models based on methods of the quantum mechanics with a finite number of degrees of freedom. The highly non-linear character of such field theory makes it very suitable to the description of complex phenomena of strong interaction and very present in several applications. In fact, using the Skyrme model, a lot of nuclear properties can be understood from a qualitative point of view, like their masses, or their spectra (corresponding to excitations of the spin and isospin of the Skyrmions). On the other hand, the quantitative precision of the standard Skyrme model does not exceed a 10-30%. The main reason for this limitation is the lack of BPS solutions in the standard Skyrme model, what implies binding energies too high and internuclear forces too strong, among other problems. To deal with these limitations, some generalizations of the Skyrme model have been studied with the same content of fields but adding new terms to the Lagrangian. Among these generalized Skyrme theories, an integrable theory with an infinite number of exact solutions (topological solitons) saturating a Bogomolny bound has been found out recently. This is the BPS Skyrme model. Due to its integrability, this model has the symmetries of an incompressible fluid. This and the BPS property make the model phenomenological suitable for nucleus description. For instance, because of the BPS property, binding energies of classical solitons are zero, and low binding energies of real nuclei are obtained by quantum corrections and by small contributions from additional terms in the Lagrangian. Soliton radii also grow with the cube root of the baryonic charge, as in real nuclei. With the purpose of studying in detail the BPS Skyrme model and its application to hadronic and nuclear physics, the following research lines have been developed: 1. The analysis of the thermodynamics of the BPS Skyrme model at zero temperature with the introduction of an external pressure and the calculation of the energymomentum tensor. Moreover, two important thermodynamical quantities like the compressibility and the baryon chemical potential were studied. 2. The introduction of the quantization of the collective coordinates (spin and isospin), as in the standard Skyrme model. Moreover, the electrostatic energy (Coulomb term) and a little explicit breaking of the isospin were added. The Coulomb term is really important for heavy nuclei, whereas isospin symmetry breaking will split the protons and neutrons. 3. The coupling of the BPS Skyrme model to gravity to describe neutron stars in good agreement with the observational constraints concerning mass and radius. Here, two distinct approaches were followed (exact and mean-field calculations) finding that, although for global properties there are not too much difference, it is not the case of local ones, where the difference is pronounced. 4. The study of the influence of several different potentials in the researches mentioned above, because the specific shape of the potential is not important for the mathematical properties. Finally, it is worth commenting that, although the BPS model gives the dominant contributions to many nuclear matter properties, some evidences have been found that an extension to a near-BPS model is needed for a complete description of strong interactions.