  The TOV equation appears as the relativistic counterpart of the classical
condition for hydrostatic equilibrium. In the present work we aim at showing
that a generalised TOV equation also characterises the equilibrium of models
endowed with other symmetries besides spherical. We apply the dual null
formalism to spacetimes with two dimensional spherical, planar and hyperbolic
symmetries with a perfect fluid as the source. We also assume a Killing vector
field orthogonal to the surfaces of symmetry, which gives us static solutions,
in the timelike Killing field case, and homogeneous dynamical solutions in the
case the Killing field is spacelike. In order to treat equally all the
aforementioned cases, we discuss the definition of a quasi-local energy for the
spacetimes with planar and hyperbolic foliations, since the Hawking-Hayward
definition only applies to compact foliations. After this procedure, we are
able to translate our geometrical formalism to the fluid dynamics language in a
unified way, to find the generalized TOV equation, for the three cases when the
solution is static, and to obtain the evolution equation, for the homogeneous
spacetime cases. Remarkably, we show that the static solutions which are not
spherically symmetric violate the weak energy condition (WEC). We have also
shown that the counterpart of the TOV equation for the spatially homogeneous
models is just the familiar equation \r{ho} + P = 0, defining a cosmological
constant-type behaviour, both in the hyperbolic and spherical cases. This
implies a violation of the strong energy condition in both cases, added to the
above mentioned violation of the weak energy condition in the hyperbolic case.
We illustrate our unified treatment obtaining analogs of Schwarzschild interior
solution, for an incompressible fluid $\rho = \rho_0$ constant.
