Particles and their fluids in nontrivial matter extensions to general relativity

Abstract: According to the standard von Laue condition, the volume-averaged pressure inside particles of fixed mass and structure vanishes in the Minkowski limit of general relativity. Here we show that this condition is in general not fulfilled in the context of $f(R,T)$ gravity, or of other theories of gravity in which the linear momentum is not conserved in this limit (here, $R$ and $T$ represent the Ricci scalar and the trace of the energy-momentum tensor, respectively). We derive a generalized von Laue condition valid for the $\mathcal R(R) + \mathcal F(T)$ subclass of $f(R,T)$ theories of gravity and discuss its cosmological implications. In particular, we show that the standard radiation and matter era evolution of the universe is recovered in the context $R + \mathcal F(T)$ gravity independently of the specific properties of the function $\mathcal F(T)$. We also find that dust -- a perfect fluid whose particles are at rest in the fluid's proper frame -- cannot in general be described as pressureless in the context of these theories. We further discuss the implications of our findings for the form of the on-shell Lagrangian of an ideal gas.