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 ESAs 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.
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