Neutrino oscillations induced by a new bumblebee black hole

TL;DR

This work analyzes neutrino propagation in the spacetime of a newly proposed bumblebee black hole arising from spontaneous Lorentz-symmetry breaking. It examines three facets: energy deposition from neutrino-antineutrino annihilation, the phase evolution of neutrino mass eigenstates in curved geometry, and flavor conversion under weak gravitational lensing, all within a two-flavor framework. The results show that the Lorentz-violating deformation χ can markedly enhance annihilation-driven energy release, induce distinct shifts in the oscillation phase, and reshape the angular pattern of lensing-induced flavor transitions, suggesting that next-generation neutrino detectors could constrain χ or reveal Lorentz-violating signals in strong gravity. The study underscores the new geometry as a potent probe of Lorentz violation in astrophysical settings and motivates further exploration, including Kalb-Ramond black holes.

Abstract

This work investigates neutrino propagation in the spacetime of a newly introduced black hole arising from spontaneous Lorentz-symmetry breaking in bumblebee gravity. The analysis focuses on three independent components: the rate at which neutrino-antineutrino annihilation deposits energy in the surrounding region, the geometric contribution to the phase accumulated by neutrino mass eigenstates, and the modifications to flavor conversion produced by weak gravitational lensing. Working with a two-flavor system, both mass orderings are examined, and the calculation incorporates the interference between distinct trajectories reaching the detector. The numerical results show that the Lorentz-violating deformation substantially increases the efficiency of the annihilation channel, produces characteristic shifts in the oscillation phase not present in earlier bumblebee configurations, and reshapes the angular dependence of the lensing-induced flavor transition pattern.

Figures (7)

• Figure 1: Behavior of the ratio, $\dot{Q}/\dot{Q}_{Newt}$, as a function of $R/M$ for different choices of the Lorentz--violating parameter $\chi$.
• Figure 2: Values of the ratio, $\dot{Q}/\dot{Q}_{Newt}$, computed at $R/M = 3,\;3.5,\;4$, and $4.5$ for several choices of the Lorentz--violating parameter $\chi$.
• Figure 3: Radial behavior of the differential deposition rate $\mathrm{d}\dot{Q}/\mathrm{d}r$ for several choices of the compactness ratio $M/R$. In the Newtonian limit ($M=0$), the expression reduces to $\mathrm{d}\dot{Q}/\mathrm{d}r = 1$ at the neutrino-sphere radius $r=R$.
• Figure 4: Illustration of neutrino paths undergoing weak gravitational deflection in a curved background. The points $S$ and $D$ represent the emission site and the detector, respectively.
• Figure 5: Transition probability $\nu_{e}\!\rightarrow\nu_{\mu}$ as a function of the azimuthal angle $\varphi$ for $\chi = 2,4 \times 10^{-5}$, evaluated at fixed mixing angles $\alpha = \pi/5$ and $\pi/6$.