  The radiative transfer equation (RTE) models the transport of light inside
photonic scattering samples such as paint, foam and tissue. Analytic
approximations to solve the RTE fail for samples with strong absorption and
dominant anisotropic scattering and predict unphysical negative energy
densities and the diffuse flux in the wrong direction. Here we fully
characterize the unphysical regions of three popular approximations to the RTE
for a slab, namely the $P_1$ approximation (or diffusion approximation), the
$P_3$ approximation, and a popular modification to $P_3$ that corrects the
forward scattering in the approximation. We find that the delta function
correction to $P_3$ eliminates the unphysical range in the forward scattering.
In addition, we compare the predictions of these analytical methods to exact
Monte Carlo simulations for the physical and unphysical regions. We present
maps of relative errors for the albedo and the anisotropy of the scatterers for
a realistic index contrast typical of a polymer slab in air and optical
thickness. The relative error maps provide a guideline for the accuracy of the
analytical methods to interpret experiments on light transport in photonic
scattering slabs. Our results show that the $P_1$ approximation is
significantly inaccurate to extract transport parameters unless the sample
scatters purely isotropic and elastic. The $P_3$ approximation exceeds $P_1$ in
terms of accuracy in its physical range for moderate absorption, and the $P_3$
with the delta function correction is the most accurate approximation
considered here for the forward direction.
