  By inelastic scattering of polarized neutrons near the (200)-Bragg
reflection, the susceptibilities and linewidths of the spin waves and the
longitudinal spin fluctuations were determined separately. By aligning the
momentum transfers q perpendicular to both \delta S_sw and the spontaneous
magnetization M_s, we explored the statics and dynamics of these modes with
transverse polarizations with respect to q. In the dipolar critical regime,
where the inverse correlation length kappa_z(T) and q are smaller than the
dipolar wavenumber q_d, we observe:(i) the static susceptibility of \delta
S_sw^T(q) displays the Goldstone divergence while for \delta S_z^T(q) the
Ornstein-Zernicke shape fits the data with a possible indication of a
thermal(mass-)renormalization at the smallest q-values, i.e. we find
indications for the predicted 1/q divergence of the longitudinal
susceptibility; (ii) the spin wave dispersion as predicted by the
Holstein-Primakoff theory revealing q_d=0.23(1)\AA^{-1}in good agreement with
previous work in the paramagnetic and ferromagnetic regime of EuS; (iii) within
experimental error, the (Lorentzian) linewidths of both modes turn out to be
identical with respect to the q^2-variation, the temperature independence and
the absolute magnitude. Due to the linear dispersion of the spin waves they
remain underdamped for q<q_d. These central results differ significantly from
the well known exchange dominated critical dynamics, but are quantitatively
explained in terms of dynamical scaling and existing data for T>=T_C. The
available mode-mode coupling theory, which takes the dipolar interactions fully
into account, describes the gross features of the linewidths but not all
details of the T- and q-dependencies. PACS: 68.35.Rh, 75.40.Gb
