  The Rossi X-ray Timing Explorer (RXTE) has demonstrated that the dynamical
variation of the X-ray emission from accreting neutron stars and stellar mass
black holes is a powerful probe of their strong gravitational fields. At the
same time, the X-ray burst oscillations at the neutron star spin frequency have
been used to set important constraints on the mass and radius of neutron stars,
hence on the equation of state of their high density cores. The X-ray Evolving
Universe Spectroscopy mission (XEUS), the potential follow-on mission to
XMM-Newton, will have a mirror aperture more than ten times larger than the
effective area of the RXTE proportional counter array (PCA). Combined with a
small dedicated fast X-ray timing detector in the focal plane (XTRA: XEUS
Timing for Relativistic Astrophysics), this collecting area will provide a leap
in timing sensitivity by more than one order of magnitude over the PCA for
bright sources, and will open a brand new window on faint X-ray sources, owing
to the negligible detector background. The use of advanced Silicon drift
chambers will further improve the energy resolution by a factor of ~6 over the
PCA, so that spectroscopic diagnostics of the strong field region, such as the
relativistically broadened Iron line, will become exploitable. By combining
fast X-ray timing and spectroscopy, XTRA will thus provide the first real
opportunity to test general relativity in the strong gravity field regime and
to constrain with unprecedented accuracy the equation of state of matter at
supranuclear density.
