Price's law for spin fields on a Schwarzschild background

In this work, we give a proof of the globally sharp asymptotic profiles forthe spin-$\mathfrak{s}$ fields on a Schwarzschild background, including thescalar field $(\mathfrak{s}=0)$, the Maxwell field $(\mathfrak{s}=\pm 1)$ andthe linearized gravity $(\mathfrak{s}=\pm 2)$. The conjectured Price's law inthe physics literature which predicts the sharp estimates of the spin $s=\pm\mathfrak{s}$ components towards the future null infinity as well as in acompact region is shown. Further, we confirm the heuristic claim by Barack andOri that the spin $+1, +2$ components have an extra power of decay at the eventhorizon than the conjectured Price's law. The asymptotics are derived via aunified, detailed analysis of the Teukolsky master equation that is satisfiedby all these components.<br

Sensitivity of neutron to proton ratio toward the high density behavior of symmetry energy in heavy-ion collisions

The symmetry energy at sub and supra-saturation densities has a great importance in understanding the exact nature of asymmetric nuclear matter as well as neutron star, but, it is poor known, especially at supra-saturation densities. We will demonstrate here that the neutron to proton ratios from different kind of fragments is able to determine the supra-saturation behavior of symmetry energy or not. For this purpose, a series of Sn isotopes are simulated at different incident energies using the Isospin Quantum Molecular Dynamics (IQMD) model with either a soft or a stiff symmetry energy for the present study. It is found that the single neutron to proton ratio from free nucleons as well as LCP's is sensitive towards the symmetry energy, incident energy as well as isospin asymmetry of the system. However, with the double neutron to proton ratio, it is true only for the free nucleons. It is possible to study the high density behavior of symmetry energy by using the neutron to proton ratio from free nucleons.Comment: 11 Pages, 9 Figure