Neutrino oscillations in a Kalb-Ramond black hole background

TL;DR

This work analyzes neutrino propagation around a Kalb-Ramond black hole, where spontaneous Lorentz violation deforms the spacetime metric via a parameter $\ell$. The authors focus on observable signatures—neutrino–antineutrino energy deposition, oscillation phases, and lensing-induced flavor transitions—and perform numerical studies in both $2$- and $3$-flavor frameworks across normal and inverted hierarchies. They find that the phase accumulates as $\Phi_k \propto (1-\frac{\ell}{2})$, increasing the oscillation length, while the energy deposition rate is systematically altered (enhanced relative to the GR baseline by a few to ~14\% depending on $\ell$). The results show measurable flavor-modulation effects in astrophysical contexts and suggest that upcoming detectors (e.g., IceCube-Gen2) could probe Lorentz-violating scales $\ell \gtrsim 10^{-10}$; future work should extend to a full quantum-field-theoretic treatment including spin-flip and decoherence in curved backgrounds.

Abstract

The analysis examines how neutrinos behave when their trajectories unfold around a black hole sourced by a Kalb-Ramond field, where spontaneous Lorentz symmetry breaking reshapes the surrounding geometry. Instead of following the conventional order, the study focuses first on the observable consequences: alterations in the neutrino-antineutrino annihilation energy output, shifts in the oscillation phase accumulated along the path, and distortions in flavor conversion probabilities induced by gravitational lensing. These features are then tied to the Lorentz-violating spacetime structure, which governs the propagation of the neutrinos. Numerical simulations are carried out for both two- and three-flavor descriptions, with normal and inverted mass orderings.

Figures (8)

• Figure 1: $\dot{Q}/\dot{Q}_{\text{Newton}}$ plotted against $\mathrm{R}/M$ for several choices of the parameter $\ell$.
• Figure 2: Radial behavior of $\mathrm{d}\dot{Q}/\mathrm{d}r$ for several values of $M/\mathrm{R}$, including the Newtonian limit where $M=0$ yields $\mathrm{d}\dot{Q}/\mathrm{d}r=1$ at $r=\mathrm{R}$.
• Figure 3: Neutrino trajectories distorted by mild gravitational lensing; $S$ denotes the emission point and $D$ the detection site.
• Figure 4: Variation of $\nu_{e}\!\rightarrow\!\nu_{\mu}$ conversion with $\varphi$ for $\ell = 1\times10^{-10}$ and $3\times10^{-10}$ under different hierarchies and mixing angles.
• Figure 5: Variation of $\nu_{e}\!\rightarrow\!\nu_{\mu}$ conversion with $\varphi$ for several $\ell$ values and mixing angles, evaluated for both mass hierarchies.