  XEUS has been recently selected by ESA for an assessment study. XEUS is a
large mission candidate for the Cosmic Vision program, aiming for a launch date
as early as 2018. XEUS is a follow-on to ESA's Cornerstone X-Ray Spectroscopy
Mission (XMM-Newton). It will be placed in a halo orbit at L2, by a single
Ariane 5 ECA, and comprises two spacecrafts. The Silicon pore optics assembly
of XEUS is contained in the mirror spacecraft while the focal plane instruments
are contained in the detector spacecraft, which is maintained at the focus of
the mirror by formation flying. The main requirements for XEUS are to provide a
focused beam of X-rays with an effective aperture of 5 m^2 at 1 keV, 2 m^2 at 7
keV, a spatial resolution better than 5 arcsec, a spectral resolution ranging
from 2 to 6 eV in the 0.1-8 keV energy band, a total energy bandpass of 0.1-40
keV, ultra-fast timing, and finally polarimetric capabilities. The High Time
Resolution Spectrometer (HTRS) is one of the five focal plane instruments,
which comprises also a wide field imager, a hard X-ray imager, a cryogenic
spectrometer, and a polarimeter. The HTRS is unique in its ability to cope with
extremely high count rates (up to 2 Mcts/s), while providing sub-millisecond
time resolution and good (CCD like) energy resolution. In this paper, we focus
on the specific scientific objectives to be pursued with the HTRS: they are all
centered around the key theme "Matter under extreme conditions" of the Cosmic
Vision science program. We demonstrate the potential of the HTRS observations
to probe strong gravity and matter at supra-nuclear densities. We conclude this
paper by describing the current implementation of the HTRS in the XEUS focal
plane.
