Abstract
The BPS Skyrme model has been demonstrated already to provide a physically intriguing and quantitatively reliable description of nuclear matter. Indeed, the model has both the symmetries and the energy–momentum tensor of a perfect fluid, and thus represents a field theoretic realization of the “liquid droplet” model of nuclear matter. In addition, the classical soliton solutions together with some obvious corrections (spin–isospin quantization, Coulomb energy, proton–neutron mass difference) provide an accurate modeling of nuclear binding energies for heavier nuclei. These results lead to the rather natural proposal to try to describe also neutron stars by the BPS Skyrme model coupled to gravity. We find that the resulting self-gravitating BPS Skyrmions provide excellent results as well as some new perspectives for the description of bulk properties of neutron stars when the parameter values of the model are extracted from nuclear physics. Specifically, the maximum possible mass of a neutron star before black-hole formation sets in is a few solar masses, the precise value of which depends on the precise values of the model parameters, and the resulting neutron star radius is of the order of 10 km.
Highlights
The calculation of physical observables of strongly interacting matter at low energies – relevant, e.g., to nuclear physics – directly from QCD is a notoriously difficult problem, which led to the introduction of low-energy effective field theories (EFTs) as a more tractable alternative
Our results are not yet final predictions of neutron star properties, because genuine predictions require the knowledge of the full near-BPS Skyrme model (1) together with the values of all its coupling constants, which should follow from an application to nuclear physics and the corresponding detailed fit to nuclear data
The full near-BPS Skyrme model may lead to a further improvement in the description of neutron stars, in the following sense
Summary
The calculation of physical observables of strongly interacting matter at low energies – relevant, e.g., to nuclear physics – directly from QCD is a notoriously difficult problem, which led to the introduction of low-energy effective field theories (EFTs) as a more tractable alternative. Skyrmions for large baryon number tend to form crystals of lower B substructures [6,7], which is at odds with the liquid-type behavior of physical heavy nuclei These problems recently led to propose several “near BPS” Skyrme models, that is, generalizations of the original Skyrme model which are close to BPS models [8,9]. The BPS Skyrme model allows for a very accurate description of nuclear binding energies [10,11], especially for heavy nuclei It is the purpose of the present letter to couple the BPS Skyrme model to gravity and to use the resulting self-gravitating BPS Skyrmions for the description of neutron stars. An accessible review can be found in [17]
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