{
  "abstract": "We show that the expressions for the matter Lagrangian \\(L_m\\) and the metric variation \\(δT_{μν}\\) of a perfect fluid obtained in previous studies appear to be inconsistent with the standard energy-momentum tensor under general conditions. Consequently, a large number of studies in astrophysics and cosmology relying on these expressions may need to be re-examined. By performing a series of straightforward calculations directly on the standard energy-momentum tensor \\(T_{μν}\\) together with the particle number conservation condition, we derive an expression for \\(δT_{μν}\\) that is independent of the choice of \\(L_m\\). Applying this result to \\(f(R,T)\\) gravity, we obtain the exact form of the tensor \\(Θ_{μν} = g^{σρ} \\frac{δT_{σρ}}{δg^{μν}}\\), which remains an important yet long-standing controversial quantity. This expression is shown to hold also for radiation, regardless of whether particle number is conserved. A major result is that if the energy-momentum tensor \\(T_{μν}\\) of the Universe consists solely of standard components (baryonic/cold dark matter, radiation, and the cosmological constant), then \\(f(R,T)\\) gravity satisfies the conservation law \\(\\nabla_μT^{μν} = 0\\) for any function \\(f(R,T)\\). This contrasts with previous studies, which found that the conservation law holds only for a restricted class of \\(f(R,T)\\) functions. Applying the same formalism to stellar interiors, we derive a class of functions that preserve the conservation law. We construct a specific \\(f(R,T)\\) model that is consistent at both cosmological scales and in high-density objects such as neutron stars. Remarkably, the same parameter set in this model simultaneously alleviates the Hubble tension and reproduces the observed mass-radius (M--R) relation of neutron stars.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Eur. Phys. J. C 86, 912 (2026)",
  "arxiv": "2610.05763",
  "author_total": 1,
  "authors": [
    {
      "name": "Pham Van Ky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbg8tr9zyymt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05763",
  "fulltext_url": null,
  "id": "fbg8tr9zyymt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05763",
  "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",
      "physics.gen-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.05763",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbg8tr9zyymt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05763",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05763"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.gen-ph",
      "subfield": "general"
    }
  ],
  "title": "Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars",
  "title_text": "Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/fbg8tr9zyymt9",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1140/epjc/s10052-026-16185-y",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}