Abstract:
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of nuclear symmetry energy leads to large changes in the binding energy of neutron stars. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then is significantly smaller than the difference resulting from variations in the symmetry energy.

Abstract:
There is a degeneracy between the equation of state (EOS) of superdense neutron-rich nuclear matter and the strong-field gravity in understanding properties of neutron stars. While the EOS is still poorly known, there are also longstanding ambiguities in choosing General Relativity or alternative gravity theories in the not-so-well tested strong-field regime. Besides possible appearance of hyperons and new phases, the most uncertain part of the nucleonic EOS is currently the density dependence of nuclear symmetry energy. To provide information that may help break the EOS-gravity degeneracy, we investigate effects of symmetry energy within its uncertain range determined by terrestrial nuclear laboratory experiments on the gravitational binding energy and spacetime curvature of neutron stars within GR and the scalar-tensor (ST) theory of gravity. In particular, we focus on effects of the following parameters characterizing the EOS of neutron-rich nucleonic matter: (1) the incompressibility $K_0$ of symmetric nuclear matter, (2) the slope $L$ of symmetry energy at saturation density and (3) the high-density behavior of symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of symmetry energy leads to large changes in both the binding energy and curvature of neutron stars while effects of varying the more constrained $K_0$ are negligibly small. The difference in predictions using the GR and the ST theory appears only for massive neutron stars, and is significantly smaller than the differences resulting from variations in the symmetry energy. We conclude that within the ST theory of gravity, the EOS-gravity degeneracy has been broken by the recent relativistic pulsar measurements, and that measurements of neutron star properties sensitive to the compactness constrain mainly the density dependence of the symmetry energy.

Abstract:
Implications of recently well-measured neutron star masses, particularly near and above 2 solar masses, for the equation of state (EOS) of neutron star matter are highlighted. Model-independent upper limits to thermodynamic properties in neutron stars, which only depend on the neutron star maximum mass, established from causality considerations are presented. The need for non-perturbative treatments of quark matter in neutron stars is stressed through studies of self-bound quark matter stars, and of nucleon-quark hybrid stars. The extent to which several well-measured masses and radii of individual neutron stars can establish a model-independent EOS through an inversion of the stellar structure equations is briefly discussed.

Abstract:
Nuclear equation of state (EoS) plays an important role in understanding the formation of compact objects such as neutron stars and black holes. The true nature of the EoS has been a matter of debate at any density range not only in the nuclear physics but also in the astronomy and astrophysics. We have constructed a database of EoSs by compiling data from the literature. Our database contains the basic properties of the nuclear EoS of symmetric nuclear matter and of pure neutron matter. It also includes the detailed information about the theoretical models, for example the adopted methods and assumptions in individual models. The novelty of the database is to consider new experimental probes such as the symmetry energy, its slope relative to the baryon density, and the incompressibility, which enables the users to check their model dependences. We demonstrate the performance of the EOSDB through the examinations of the model dependence among different nuclear EoSs. It is reveled that some theoretical EoSs, which is commonly used in astrophysics, do not satisfactorily agree with the experimental constraints.

Abstract:
It is shown that a gauged SO(3) family symmetry can suppress flavor-changing processes from squark-mass non-degeneracy to an acceptable level. The potentially dangerous SO(3) D-terms can be rendered harmless if the CP-violating phases appearing in the SO(3)-breaking sector are small, which can naturally be the case if CP is a spontaneously broken symmetry. This approach has certain advantages over models based on global or non-abelian discrete symmetries, and dovetails with some recent proposals for explaining the pattern of quark and lepton masses. Moreover this approach relates the near-degeneracy of the squark masses to an approximate CP invariance which can also explain the smallness of the electron and neutron electric dipole moments.

Abstract:
The elliptic-flow ratio of neutrons with respect to protons in reactions of neutron rich Heavy-Ion at intermediate energies has been recently proposed as an observable sensitive to the strength of the symmetry term in the nuclear equation of state (EOS) at supra-saturation densities. The recent results obtained from the existing FOPI/LAND data for 197Au+197Au collisions at 400 MeV/nucleon in comparison with the UrQMD model allowed a first estimate of the symmetry term of the EOS but suffer from a considerable statistical uncertainty. In order to obtain an improved data set for Au+Au collisions and to extend the study to other systems, a new experiment was carried out at the GSI laboratory by the ASY-EOS collaboration in May 2011.

Abstract:
The recently discovery of a massive neutron star (PSR J1614-2230 of $1.97\pm0.04M_{\odot}$) rules out the soft equation of states (EOSs) such as those included hyperons or kaon condensates at high densities, while the nuclear theory or the terrestrial laboratory data prefer a soft EOS. Here we propose one possible mechanism to allow that the observed massive neutron star can be supported by a soft EOS, that is, if the the gravitational constant $G$ varies at super strong field, a soft EOS can support the massive neutron stars.

Abstract:
We study the class of pulsating strings on AdS4×ℂℙ3. Using a generalized ansatz for pulsating string configurations we find new solutions of this class. Further we quasiclassically quantize the theory and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual 𝒩=6 Chern-Simons theory.

Abstract:
In this contribution nuclear constraints on the equation of state for a neutron star are discussed. A combined fit to nuclear masses and charge radii leads to improved values for the symmetry energy and its derivative at nuclear saturation density, $S_{\rm{v}}= 31$ MeV and $L=68\pm 8$ MeV. As an application the sensitivity of some properties of rotating supramassive neutron stars on the EoS is discussed.

Abstract:
We study the sensitivity of the sound speed to relativistic corrections of the equation of state (EOS) in the standard solar model by means of a helioseismic forward analysis. We use the latest GOLF/SOHO data for $\ell = 0,1,2,3$ modes to confirm that the inclusion of the relativistic corrections to the adiabatic exponent $\Gamma_1$ computed from both OPAL and MHD EOS leads to a more reliable theoretical modelling of the innermost layers of the Sun.