The Stability Of Neutron Stars In Rastall Gravity

Neutron stars are a class of extremely compact celestial bodies in the universe,which are characterized by high density,high temperature,strong gravitational field and strong magnetic field.Therefore,the study for them can help the researchers understand the physical properties of matter under extreme conditions.In 1972,Peter Rastall proposed a theory of gravity,in which the energy-momentum tensor is not conserved.It is called Rastall gravity.In recent years,the neutron stars in Rastall gravity have been studied.According to the hydrostatic equilibrium equation in Rastall gravity(RTOV equation),there exit the stable neutron stars in Rastall gravity,for the parameter of Rastall gravity?(-?,-1)?[1,+?).This paper studies the quasi-normal modes of the static spherically symmetric neutron stars in Rastall gravity.The quasi-normal modes refer to a kind of characteristic signals which oscillate and damp.They are determined by the characteristic parameters of neutron stars.So,we can further study the material properties and stability of neutron stars by their quasi-normal modes.This paper is divided into five chapters.In Chapter 1,we elaborate the history of neutron stars and the significance of quasi-normal modes for neutron stars.In Chapter2,firstly,we discuss the gravitational field perturbation of neutron stars in general relativity,and derive the axial perturbation equation of neutron stars in general relativity.Secondly,the quasi-normal modes with=2?3?4?5 are calculated by using the polytropic equation of state.Finally,the numerical results mean that the static spherically symmetric neutron stars are stable.We also find that for the same,the numerical values of quasi-normal modes also have little difference with the same mass and different.In Chapter 3,we introduce Rastall gravity,and discuss the possible Lagrangians of Rastall gravity.In Chapter 4,we derive the axial perturbation equation of the neutron stars in Rastall gravity.Using the equation of state of the AV18,we numerically calculate the quasi-normal modes of the neutron stars with=2?3?4?5 in Rastall gravity.We find that all of?_I are more than zero in the case of??1 or?<-1,which mean that the static spherically symmetric neutron stars are stable in Rastall gravity.We also find that when=2 or=3,in the case of??1,the difference in numerical values of quasi-normal modes is very small with the same mass and different.But in the case of?<-1,it is large with the same mass and different.For=4 or=5,whether??1 or?<-1,the numerical values of quasi-normal modes also have little difference with the same mass and different.In Chapter5,we summarize the work and results of this paper,and look forward to the future research.