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ISSN: 1434-6044, SCIE

Metric variation of the energy-momentum tensor of a perfect fluid and its applications to cosmology and neutron stars

Pham Van Ky

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 = ( + P)uμuν − Pgμν 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 μν = 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 energymomentum tensor Tμν of theUniverse consists solely of standard components with EOS P = ω where ω = 0, 1/3, or −1 (baryonic/cold darkmatter, 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.