Aspects of neutrino oscillation in alternative gravity theories

Abstract

Neutrino spin and flavour oscillation in curved spacetime have been studied for the most general static spherically symmetric configuration. Having exploited the spherical symmetry we have confined ourselves to the equatorial plane in order to determine the spin and flavour oscillation frequency in this general set-up. Using the symmetry properties we have derived spin oscillation frequency for neutrino moving along a geodesic or in a circular orbit. Starting from the expression of neutrino spin oscillation frequency we have shown that even in this general context, in high energy limit the spin oscillation frequency for neutrino moving along circular orbit vanishes. We have verified previous results along this line by transforming to Schwarzschild coordinates under appropriate limit. This finally lends itself to the probability of neutrino helicity flip which turns out to be non-zero. While for neutrino flavour oscillation we have derived general results for oscillation phase, which subsequently have been applied to three different gravity theories. One, of them appears as low-energy approximation to string theory, where we have an additional field, namely, dilaton field coupled to Maxwell field tensor. This yields a realization of Reissner-Nordström solution in string theory at lowenergy. Next one corresponds to generalization of Schwarzschild solution by introduction of quadratic curvature terms of all possible form to the Einstein-Hilbert action. Finally, we have also discussed regular black hole solutions. In all these cases the flavour oscillation probabilities can be determined for solar neutrinos and thus can be used to put bounds on the parameters of these gravity theories. While for spin oscillation probability, we have considered two cases, Gauss-Bonnet term added to the Einstein-Hilbert action and the f(R) gravity theory. In both these cases we could impose bounds on the parameters which are consistent with previous considerations. In a nutshell, in this work we have presented both spin and flavour oscillation frequency of neutrino in most general static spherically symmetric spacetime, encompassing a vast class of solutions, which when applied to three such instances in alternative theories for flavour oscillation and two alternative theories for spin oscillation put bounds on the parameters of these theories. Implications are also discussed. * sumanta@iucaa.in †

Reissner–Nordstrøm–de Sitter manifold: photon sphere and maximal analytic extension

“…null geodesics orbiting the black hole at fixed r. It is known that this phenomenon is an important part of black hole spacetimes geometry. Discussions of photon orbits and there effects can be found in [6,7,8,13] for example. The effect of photon sphere concerning decay of test fields can be seen in [1,3,17] among others.…”

“…Instead of finding s 1 and s 2 explicitly, we will, using the next lemma, transform the conditions in (7) to those in (5) directly.…”

On some novel features of the Kerr–Newman-NUT spacetime

“…Following such implications in mind, there have been attempts to study circular timelike geodesics in presence of NUT parameter [14][15][16] 1 as well as motion of charged particles in this spacetime [17]. Various weak field tests, e.g., perihelion precession, Lense-Thirring effect has also been discussed [18][19][20] (for a taste of these weak field tests in theories beyond general relativity, see [21][22][23][24][25]). We would like to emphasize that most of these studies on the geodesic motion crucially hinges on the equatorial plane, however there can also be interesting phenomenon when off-the-equatorial plane motion is considered.…”

Neutrino spin oscillations in external fields in curved spacetime

“…[8,9], was applied in Refs. [10,11] to study neutrino spin oscillations in various gravitational backgrounds. The method for the description of the particle spin evolution in a gravitational field, based on the analysis of the Dirac equation in curved spacetime, was recently developed in Ref.…”