Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time

Details Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time

2004-01-11

arxiv.org/abs/gr-qc/0401044v3

Phys. Rev. D71 (2005) 105003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTeX 4.0 file; 15 pages, no figures

Scientific paper

10.1103/PhysRevD.71.105003

We study the helicity and chirality transitions of a high-energy neutrino propagating in a Schwarzschild space-time background. Using both traditional Schwarzschild and isotropic spherical co-ordinates, we derive an ultrarelativistic approximation of the Dirac Hamiltonian to first-order in the neutrino's rest mass, via a generalization of the Cini-Touschek transformation that incorporates non-inertial frame effects due to the noncommutative nature of the momentum states in curvilinear co-ordinates. Under general conditions, we show that neutrino's helicity is not a constant of the motion in the massless limit due to space-time curvature, while the chirality transition rate still retains an overall dependence on mass. We show that the chirality transition rate generally depends on the zeroth-order component of the neutrino's helicity transition rate under the Cini-Touschek transformation. It is also shown that the chiral current for high-energy neutrinos is altered by corrections due to curvature and frame-dependent effects, but should have no significant bearing on the chiral anomaly in curved space-time. We determine the upper bound for helicity and chirality transitions near the event horizon of a black hole. The special case of a weak-field approximation is also considered, which includes the gravitational analogue of Berry's phase first proposed by Cai and Papini. Finally, we propose a method for estimating the absolute neutrino mass and the number of right-handed chiral states from the expectation values of the helicity and chirality transition rates in the weak-field limit.

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