Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars
Abstract
We show that the expressions for the matter Lagrangian Lm and the metric variation δTμν 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 Tμν together with the particle number conservation condition, we derive an expression for δTμν that is independent of the choice of Lm. Applying this result to f(R,T) gravity, we obtain the exact form of the tensor Θμν = gσρ δTσρ/δgμν, 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 Tμν 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 ∇μTμν = 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.
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BibTeX
@misc{ky2026metric,
title = {{Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars}},
author = {Pham Van Ky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05763},
eprint = {2610.05763},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05763},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars
AU - Pham Van Ky
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05763
UR - https://arxiv.org/abs/2610.05763
AB - 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 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 ∇_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.
ER -