  We present a tetrad-based method for solving the Einstein field equations for
spherically-symmetric systems and compare it with the widely-used
Lema\^itre-Tolman-Bondi (LTB) model. In particular, we focus on the issues of
gauge ambiguity and the use of comoving versus 'physical' coordinate systems.
We also clarify the correspondences between the two approaches, and illustrate
their differences by applying them to the classic examples of the Schwarzschild
and Friedmann-Robertson-Walker spacetimes. We demonstrate that the tetrad-based
method does not suffer from the gauge freedoms inherent to the LTB model,
naturally accommodates non-zero pressure and has a more transparent physical
interpretation. We further apply our tetrad-based method to a generalised form
of 'Swiss cheese' model, which consists of an interior spherical region
surrounded by a spherical shell of vacuum that is embedded in an exterior
background universe. In general, we allow the fluid in the interior and
exterior regions to support pressure, and do not demand that the interior
region be compensated. We pay particular attention to the form of the solution
in the intervening vacuum region and verify the validity of Birkhoff's theorem
at both the metric and tetrad level. We then reconsider critically the original
theoretical arguments underlying the so-called $R_h = ct$ cosmological model,
which has recently received considerable attention. These considerations in
turn illustrate the interesting behaviour of a number of 'horizons' in general
cosmological models.
