Consistent energy-momentum trace couplings of fluids

Abstract

Gravitational models with non-minimal couplings involving the trace of the energy-momentum tensor have become increasingly popular. The idea of coupling the trace of the matter tensor to the geometry can be applied to various matter models, including relativistic perfect fluids. However, it is well-known that the variational formulation of perfect fluids involves some technicalities. We carefully derive the field equations including the trace coupling of a perfect fluid using two different approaches, namely, that given by Brown using Lagrange multipliers, and that given by Schutz using velocity potentials. We show that previous results involving such trace couplings do not match the results presented here. We demonstrate that our fluid's equations of motion are consistent with the gravitational field equations. Moreover, we present a simple on-shell argument which further supports the correctness of our results. Our work implies that a vast amount of the $f(R,T)$ literature using perfect fluids needs to be revisited.

v1 28 pages; v2 31 pages, 2 new subsections, updated references

References in corpus (10)

• f(R,T) gravity
• Extra force in $f(R)$ modified theories of gravity
• Action functionals for relativistic perfect fluids
• Nonminimal coupling of perfect fluids to curvature
• Large-scale curvature and entropy perturbations for multiple interacting fluids
• Adiabatic and entropy perturbations with interacting fluids and fields
• Reexamining $f(R,T)$ gravity
• Field Theories and Fluids for an Interacting Dark Sector
• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• On-shell Lagrangian of an ideal gas

Cited by in corpus (4)

• Density perturbations in nonminimally coupled gravity: symptoms of Lagrangian density ambiguity
• Energy conditions in consistent perfect fluid cosmology
• Lagrangian Identity and Mass Evolution of Particle-like Objects in Nonminimally Coupled Gravity
• Quantum Cosmology in $f(R,T)$ Theory with Schutz's Perfect Fluid