{
  "abstract": "We present a fully nonlinear relativistic description of the observed pulsar timing modulations, defined through the ratio of the proper-time intervals between two successive emissions of radio pulses and their observations by a pulsar timing array. Working in the limit of a vanishing emission interval, we derive the observed pulsar timing modulation to second order in relativistic perturbation theory around a Minkowski background, without fixing a gauge and retaining the full scalar, vector, and tensor content of the metric perturbations. Although the derivation naturally introduces several gauge-dependent intermediate quantities, we explicitly demonstrate that they combine into a coordinate-independent expression. Moreover, we explicitly show that the second-order timing modulation from two neighboring radio pulses coincides with the observed redshift, defined as the fractional change in wavelength along a single geodesic. The agreement represents a nontrivial second-order realization of the exact nonlinear equivalence proven in Magi & Yoo 2026.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13364",
  "author_total": 2,
  "authors": [
    {
      "name": "Matteo Magi"
    },
    {
      "name": "Jaiyul Yoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wg5t307yp570.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13364",
  "fulltext_url": null,
  "id": "3wg5t307yp570",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13364",
  "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",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7213368801",
  "pdf_url": "https://arxiv.org/pdf/2609.13364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wg5t307yp570.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13364"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Complete Second-Order Relativistic Derivation of the Observed Pulsar Timing Modulations",
  "title_text": "Complete Second-Order Relativistic Derivation of the Observed Pulsar Timing Modulations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/3wg5t307yp570",
  "venue": "arXiv",
  "versions": []
}