{
  "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 $|\\widehat e(ω,r_c)|\\propto(γ_c-γ)^{-1/2}$, while the propagating monopole remains regular. For higher multipoles we obtain the exact axial zero-mode tower $ξ_{\\ell n}=-(\\ell+n+1)(\\ell+n+2)/3$. At $\\ell=1$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39936",
  "author_total": 4,
  "authors": [
    {
      "name": "Hong-Da Lyu"
    },
    {
      "name": "Zhi Xiao"
    },
    {
      "name": "Zhong-Xi Yu"
    },
    {
      "name": "Shoulong Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dw8fr028s0zwr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39936",
  "fulltext_url": null,
  "id": "dw8fr028s0zwr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39936",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7215030817",
  "pdf_url": "https://arxiv.org/pdf/2609.39936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dw8fr028s0zwr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.39936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39936"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background",
  "title_text": "Zero modes and oscillatory instabilities of a Lorentz-violating Kalb-Ramond field on a Schwarzschild background",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/dw8fr028s0zwr",
  "venue": "arXiv",
  "versions": []
}