  We have identified three possible ways in which future XMM-Newton
observations can provide significant constraints on the equation of state of
neutron stars. First, using a long observation of the neutron star X-ray
transient CenX-4 in quiescence one can use the RGS spectrum to constrain the
interstellar extinction to the source. This removes this parameter from the
X-ray spectral fitting of the pn and MOS spectra and allows us to investigate
whether the variability observed in the quiescent X-ray spectrum of this source
is due to variations in the soft thermal spectral component or variations in
the power law spectral component coupled with variations in N_H. This will test
whether the soft thermal spectral component can indeed be due to the hot
thermal glow of the neutron star. Potentially such an observation could also
reveal redshifted spectral lines from the neutron star surface. Second,
XMM-Newton observations of radius expansion type I X-ray bursts might reveal
redshifted absorption lines from the surface of the neutron star. Third,
XMM-Newton observations of eclipsing quiescent low-mass X-ray binaries provide
the eclipse duration. With this the system inclination can be determined
accurately. The inclination determined from the X-ray eclipse duration in
quiescence, the rotational velocity of the companion star and the
semi-amplitude of the radial velocity curve determined through optical
spectroscopy, yield the neutron star mass.
