Mass Neutrino Oscillation And Gravitational Redshift

Many deductions can be obtained from Einstein's gravitational field equation, some of these deductions can not be interpreted by Newtonian mechanics, others which have more or less the physical interpretation are called gravitational effects. In this paper, we concentrate on two effects: interference phase of mass neutrino in gravitational field of central mass with electric and magnetic charge and magnetic moment(CM space-time) and surface redshift for an anisotropic and spherically symmetric star in the presence of cosmological constant.With highly confident atmospheric neutrino experiment of Super-Kamiokande to assure the neutrino mass, the mass neutrino oscillation has been probed with intense theoretical and experimental vigor, especially it's characteristics in curved space-time. Taking the gravitational background into account, the physics related to the neutrino oscillation in Minkowski space-time with Lorentz invariant will be extended to Riemannian space-time with general coordinate transformation. Moreover, in 1958, Pontecorvo pointed out that if the mass of neutrino is nonzero, the dieffrent kind of neutrinos will transform commutatively, so the mass neutrino oscillation happens. From the quantum meehanics of neutrino oscillation we known that at the detector point the oscillation probability of one kind of neutrino transforming into another is relative to the mixing angle, the average energy of the neutrino beam, the source-detector distnance and the mass-squared dieffrence between two kinds of neutrinos. After we extend the calculation of interference phase of mass neutrino in flat space-time to that of curved space-time, we give the expression of the interference phase of mass neutrino in CM space-time, alonging the geodesic in radial direction. From the expression, we derive the conclusion that the phase is relevant to the electric and magnetic charges and magnetic moment of the central mass, as well as the energe of the neutrino and the inherent distance beween gravitational source and detector.The gravitational redshift of spectral lines is one of the most famous classical gravitational effects which were verified by experiments, it verified the equivalence principle which is the basic principle of general relativity. The dependence of grav- itational redshift on different gravitational parameters makes it have many characteristics. It is well known that the surface redshift z for a static perfect fluid sphere, whose density is positive and not increasing outwards, is not larger than z_m = 2. In the third chapter, we derive the inequality which limits the mass- radius ratio for anisotropic general relativistic matter distributions in the presence of a cosmological constant and energy condition. From this inequality, we display that the surface redshift z obeys the inequality (?), whereΛis cosmological constant and (?) is the average energy density of the celestial body, then it is easy to see that the maximum value of surface redshift is less than 2.