  We investigate the behaviour of the Tolman metrics within the formalism of
the trace-free (or unimodular) gravity. While this approach is similar to the
standard Einstein field equations, some subtlety arises. The effective number
of independent field equations is reduced by one on account of the density and
pressure appearing as an inseparable entity the inertial mass density. Further
energy is not conserved within the trace-free theory but the conservation law
may be supplemented to the field equations. This presentation of the field
equations offers a different avenue to determine the density and pressure
explicitly. It turns out that an extra integration constant is always in
evidence. While this constant has little impact on the dynamics and energy
conditions, it makes a significant impact on the gravitational mass and
equation of state. Graphical plots are generated to analyse the behaviour of
physical quantities qualitatively.
