Accelerating imperfect fluid

TL;DR

This paper explores the effects of inhomogeneous, accelerating fluids on spacetime geometry, introducing a velocity-dependent gravitational potential and analyzing geodesic equations, revealing unique energy density and pressure behaviors.

Contribution

It introduces a velocity-dependent semiclassical gravitational potential obeying a Yukawa-type equation for inhomogeneous fluids in accelerated motion.

Findings

Fluid has zero energy density for perfect fluid component

Nonzero anisotropic energy density observed

Pressures become independent of quantum effects over long times

Abstract

An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A velocity-dependent semiclassical gravitational potential is introduced, which obeys an Yukawa-type equation, written in Cartesian coordinates. The timelike and null geodesic equations are investigated. One finds that the fluid has zero energy density corresponding to the perfect fluid part but nonzero anisotropic energy density. The pressures will no longer depend on $\hbar$ for time intervals $t>>1/m$, where $m$ is the field mass.