There are many rotating spheroids in the universe. Since the times of Newton, many astronomers and physicists have studied them. They have used theoretical methods (mainly as moment methods) to study their gravitational properties. One important question, however, is whether people can investigate gravitational properties of the stars from observations. Can we use the geodesy motion of microscopic particles (such as photons and electrons) in the equatorial plane and their scatterings to obtain the basic properties of the stars, such as stellar mass, radius and average density? The answer is yes.

For the first time in the past two years, Prof. Zhi-Fu Gao from the Pulsar Group of Xinjiang Astronomical Observatory and Dr. Ci-Xing Chen from University of Science and Technology of China gave different solutions of Dirac equation in a curved space of rotating ellipsoidal stars (eight quantum energy states corresponding to Dirac spinors in the weak gravitational field approximation respectively). They studied the scattering cross sections and scattering amplitudes of the Dirac spinors and obtained a general expression for the scattering crosses. The research took the gravitational potentials in a simplified Maclaurin sphere model and obtained the scattering amplitudes of Dirac spinors in a curved space using a long but straightforward calculation in the long-wave approximation. Their results have shown that the sensitivity of the scattering cross to the change of stellar density is proportional to the density. This study focused on the establishment of a physical model for Dirac spinor scattering. It is expected that our results can be compared with the future observations (such as scattering cross section and geodesic, stable orbit and so on) thus providing tests and improvements to our theoretical model (Notice that the future data referred here can be obtained from observations, or they can be obtained directly from building other physical models that combined with other quantities).

This study was published in the well-known international journal “The European Physical Journal C：field theory and particle physics ” ( Eur. Phys. J. C, 2020, 80：582). The results can be applied to white dwarfs, main sequence stars, red giants, red supergiant stars and so on, provided that the matter inside these stars is composed of low-density, incompressible fluid, and the gravitational field is very weak, so that it can be treated by the Newton approximation. The innovation of this study lies in the building of a new way to study the gravitational properties of rotating spheroids and to reveal the mystery of the gravity of rotating spheroids.