Effects of bumblebee gravity on neutrino motion

TL;DR

The paper investigates how spontaneous Lorentz violation in a Bumblebee gravity background affects neutrino dynamics near a Schwarzschild-like black hole. It combines analytic derivations of neutrino pair annihilation energy deposition, phase evolution, and gravitational lensing with numerical two-flavor simulations to assess flavor transitions under normal and inverted mass orderings, and contrasts the results with a Kalb-Ramond Lorentz-violating background. Key findings show that the Lorentz-violating parameter $\ell$ increases the annihilation energy deposition by several percent to over ten percent for representative parameters, lengthens the neutrino oscillation phase, and can boost flavor conversion probabilities by up to ~20%, with pronounced azimuthal and mass-ordering dependencies. The results suggest that upcoming neutrino observatories could, in principle, probe such Lorentz-violating backgrounds in extreme astrophysical settings, providing a pathway to test fundamental symmetry breaking in strong gravity.

Abstract

This study explores how the spontaneous violation of Lorentz symmetry -- modeled through a black hole solution in the context of bumblebee gravity -- affects the propagation and dynamics of neutrinos. The investigation centers on three distinct aspects: the rate of energy deposition due to neutrino-antineutrino pair annihilation, modifications to the neutrino oscillation phase driven by the underlying spacetime structure, and the influence of gravitational lensing on flavor conversion probabilities. To support the theoretical considerations, numerical simulations are conducted for oscillation probabilities in a two-flavor framework, taking into account both normal and inverted mass orderings. For comparison, the outcomes are juxtaposed with those obtained in a different Lorentz-violating background, namely, a black hole solution within Kalb-Ramond gravity.

Figures (6)

• Figure 1: The plot displays the behavior of the ratio $\dot{Q}/\dot{Q}_{\text{Newton}}$ as a function of $R/M$, considering different values of the Lorentz--violating parameter $\ell$.
• Figure 2: The radial profile of the differential energy deposition rate, $\mathrm{d}\dot{Q}/\mathrm{d}r$, is analyzed for different values of the compactness ratio $M/R$. In the Newtonian regime—corresponding to the case where $M = 0$—the relation reduces to a simpler form, resulting in $\mathrm{d}\dot{Q}/\mathrm{d}r = 1$ precisely at the boundary $r = R$.
• Figure 3: The illustration demonstrates the influence of weak gravitational lensing on neutrino trajectories within a curved spacetime background. The location denoted by $S$ represents the source of emission, while the point marked $D$ corresponds to the position of the detector.
• Figure 4: The transition probability $\nu_e \to \nu_\mu$ is examined with respect to variations in the azimuthal angle $\varphi$, focusing on two specific values of the Lorentz--violating parameter: $\ell = 1\times10^{-10}$ and $\ell = 3\times10^{-10}$. The analysis is conducted within the framework of two--flavor neutrino oscillations, incorporating both normal and inverted mass hierarchies. Two different mixing angles, $\alpha = \pi/5$ and $\alpha = \pi/6$, are also considered to explore how the conversion behavior responds to changes in the oscillation parameters.
• Figure 5: The flavor conversion probability $\nu_e \to \nu_\mu$ is explored as it varies with the azimuthal angle $\varphi$, using different values of the Lorentz--violating parameter, $\ell = 0, 1\times10^{-10}, 2\times10^{-10}$ and $3\times10^{-10}$. This study is performed within the context of a two-flavor oscillation framework, incorporating both normal and inverted mass hierarchies. The influence of the mixing angle is examined by selecting $\alpha = \pi/5$ and $\alpha = \pi/6$ as benchmark values.