{
  "abstract": "We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight $s=2$, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For $s\\neq0$ the fields $Ψ^{(s)}$ and $Ψ^{(-s)}$ are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate $Ψ^{(-2)}$ to a fourth-order operator on $Ψ^{(2)}$ and yield an $H^2$ energy norm after symmetrization. With the $H^1$ norm known for $s=0$, this suggests the pattern $H^{|s|}$, verified for $s=0$ and $s=2$. All results use an $ω$-independent two-field hierarchy. We find that the pseudospectrum tightens by $1.1$ to $3.5$ decades at each step of $L^2\\to H^1\\to H^2$, yet stays large in every norm. The $s=+2$ and $s=-2$ operators are isospectral but not isopseudospectral: at twelve of fourteen probes the $ψ_0$ resolvent exceeds the $ψ_4$ one by $0.19$ to $0.82$ decades in the $H^2$ norm, while at the two probes furthest along the QNM line the ordering reverses by $0.18$ to $0.19$ decades. The gravitational pseudospectrum exceeds the scalar one by $0.5$ to $5.2$ decades in the window minimum and by $5.9$ decades in $L^2$ at $ωM=0.47-0.17\\,i$, while along the damping direction the $s=2$ resolvent is non-monotonic and the $s=0$ resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06954",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongsheng Zhang"
    },
    {
      "name": "Zong-Kuan Guo"
    },
    {
      "name": "Rong-Gen Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b35gd66p21qqq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06954",
  "fulltext_url": null,
  "id": "b35gd66p21qqq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06954",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.HE"
    ],
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7221015895",
  "pdf_url": "https://arxiv.org/pdf/2610.06954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b35gd66p21qqq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.06954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06954"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The pseudospectrum for gravitational perturbations in Kerr spacetimes",
  "title_text": "The pseudospectrum for gravitational perturbations in Kerr spacetimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/b35gd66p21qqq",
  "venue": "arXiv",
  "versions": []
}