Neutrino Spin Oscillations in Gravitational Fields

Abstract

We study neutrino spin oscillations in gravitational fields. The quasi-classical approach is used to describe the neutrino spin evolution. First we examine the case of a weak gravitational field. We obtain the effective Hamiltonian for the description of neutrino spin oscillations. We also receive the neutrino transition probability when a particle propagates in the gravitational field of a rotating massive object. Then we apply the general technique to the description of neutrino spin oscillations in the Schwarzschild metric. The neutrino spin evolution equation for the case of the neutrino motion in the vicinity of a black hole is obtained. The effective Hamiltonian and the transition probability are also derived. We examine the neutrino oscillations process on different circular orbits and analyze the frequencies of spin transitions. The validity of the quasi-classical approach is also considered.

Spin in stationary gravitational fields and rotating frames

“…The same equation has been later obtained in Ref. [4]. Here we present a rigorous deduction of the Pomeransky-Khriplovich (PK) equation of motion of the three-component spin, confirming the heuristic arguments of [3].…”

“…The corresponding equation of motion of the fourcomponent spin used in Refs. [3,4] and many other works is very similar:…”

“…Unlike Ref. [4], our derivation can be easily extended on any external fields (electromagnetic, gravitational, scalar, whatever).…”

“…Such a tetrad was used by Pomeransky and Khriplovich [3] and Dvornikov [4]. In the framework of our current study, we choose the Schwinger gauge by specifying the coframe as (9).…”

“…The extra Lorentz factor is due to the fact that the classical evolution of spin was measured by using the proper time τ, whereas the quantum evolution was analyzed by using the coordinate time t. If we choose another tetrad by putting ξ = 1/2 in (50), the equation (49) yields the result by Pomeransky and Khriplovich [3] and Dvornikov [4]:…”