Programme

P.12 -- Posters, VCTP-51

Date: Tuesday, 4 August 2026

Time: 09:30 - 10:30

Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars

Pham Van Ky

Institute of physics, Vietnam academy of science and technology (VAST)

Previous studies have proposed specific forms for the matter Lagrangian \(L_m\) and the metric variation \(\delta T_{\mu\nu}\) of a perfect fluid. However, we show in this work that these expressions are inconsistent with the standard energy-momentum tensor \(T_{\mu\nu} = (\epsilon + P) u_\mu u_\nu - P g_{\mu\nu}\) under general conditions. As a result, a substantial body of work in cosmology and astrophysics based on these formulations requires careful re-evaluation. We derive an explicit expression for the metric variation \(\delta T_{\mu\nu}\) by performing direct calculations on the standard perfect-fluid energy-momentum tensor, incorporating only the particle number conservation law. The obtained formula is completely independent of the choice of matter Lagrangian \(L_m\). Applying this result to \(f(R,T)\) gravity yields the precise form of the tensor \(\Theta_{\mu\nu} = g^{\sigma\rho} \frac{\delta T_{\sigma\rho}}{\delta g^{\mu\nu}}\), which has long been a source of controversy in the literature. This expression remains valid for radiation as well, regardless of whether particle number conservation is imposed. A central finding of this study is that when the cosmic energy-momentum tensor contains only standard components obeying linear equations of state \(P = \omega \epsilon\) with \(\omega = 0\) (baryonic and cold dark matter), \(\omega = 1/3\) (radiation), and \(\omega = -1\) (cosmological constant), the conservation law \(\nabla_\mu T^{\mu\nu} = 0\) holds for \emph{arbitrary} functions \(f(R,T)\). This contrasts sharply with earlier conclusions that restricted the allowed forms of \(f(R,T)\). We further apply the derived \(\Theta_{\mu\nu}\) to stellar interiors and obtain a family of \(f(R,T)\) models that preserve energy-momentum conservation for a polytropic equation of state. A concrete model is constructed that remains consistent across both cosmological scales and high-density regimes inside neutron stars. Notably, the same set of parameters simultaneously alleviates the Hubble tension and accurately reproduces the observed mass-radius relation of neutron stars, including the maximum mass and corresponding radius.

Presenter: Pham Van Ky