Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background
Abstract
We study equilibrium configurations and linear perturbations of a Lorentz-violating Kalb--Ramond field with a quartic symmetry-breaking potential and a non-minimal Riemann coupling on a fixed Schwarzschild background. The electric equilibrium is determined algebraically by a characteristic function that can develop a finite-radius double root. Approaching this configuration, the electric monopole response scales as |ê(ω,rc)|∝(γc−γ)−1/2, while the propagating monopole remains regular. For higher multipoles we obtain the exact axial zero-mode tower ξℓ n=−(ℓ+n+1)(ℓ+n+2)/3. At ℓ=1 a complementary static mode gives a second low-frequency branch. Increasing the positive Riemann coupling causes two purely imaginary growing modes to collide and form an oscillatory unstable pair, with square-root real-part splitting. Independent numerical checks confirm that this behavior persists under changes of the equilibrium parameters. The corrected bare sign removes the monopole ghost, but a constrained high-momentum negative-energy direction remains on the asymptotically electric branch. We therefore distinguish the existence of classical growing modes from the stronger requirement of a positive-energy theory.
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BibTeX
@misc{lyu2026zero,
title = {{Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background}},
author = {Hong-Da Lyu and Zhi Xiao and Zhong-Xi Yu and Shoulong Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39936},
eprint = {2609.39936},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39936},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background
AU - Hong-Da Lyu
AU - Zhi Xiao
AU - Zhong-Xi Yu
AU - Shoulong Li
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2609.39936
UR - https://arxiv.org/abs/2609.39936
AB - We study equilibrium configurations and linear perturbations of a Lorentz-violating Kalb--Ramond field with a quartic symmetry-breaking potential and a non-minimal Riemann coupling on a fixed Schwarzschild background. The electric equilibrium is determined algebraically by a characteristic function that can develop a finite-radius double root. Approaching this configuration, the electric monopole response scales as |ê(ω,r_c)|∝(γ_c−γ)^−1/2, while the propagating monopole remains regular. For higher multipoles we obtain the exact axial zero-mode tower ξ_ℓ n=−(ℓ+n+1)(ℓ+n+2)/3. At ℓ=1 a complementary static mode gives a second low-frequency branch. Increasing the positive Riemann coupling causes two purely imaginary growing modes to collide and form an oscillatory unstable pair, with square-root real-part splitting. Independent numerical checks confirm that this behavior persists under changes of the equilibrium parameters. The corrected bare sign removes the monopole ghost, but a constrained high-momentum negative-energy direction remains on the asymptotically electric branch. We therefore distinguish the existence of classical growing modes from the stronger requirement of a positive-energy theory.
ER -