  The covariant Vlasov-Maxwell system is used to study breaking of relativistic
warm plasma waves. The well-known theory of relativistic warm plasmas due to
Katsouleas and Mori (KM) is subsumed within a unified geometric formulation of
the `waterbag' paradigm over spacetime. We calculate the maximum amplitude
$E_\text{max}$ of non-linear longitudinal electric waves for a particular class
of waterbags whose geometry is a simple 3-dimensional generalization (in
velocity) of the 1-dimensional KM waterbag (in velocity). It is well known that
the value of $\lim_{v\to c}E_\text{max}$ (with the effective temperature of the
plasma electrons held fixed) diverges for the KM model; however, we show that a
certain class of simple 3-dimensional waterbags yields a finite value for
$\lim_{v\to c}E_\text{max}$, where $v$ is the phase velocity of the wave and
$c$ is the speed of light.
