Black holes play a key role in the evolution of galaxies and ultimately in the star formation history, but they also distort the shape of space in their vicinity. X-rays resulting from accretion of matter onto a compact object (a supermassive or stellar mass black hole, or neutron star) probe the motion of matter in strongly curved space time, in which general relativity is no longer a small correction to the classical laws of motion. This is a regime in which fundamental predictions of general relativity are still to be tested, such as the existence of an event horizon for black holes, or the dragging of inertial frames. These predictions cannot be confirmed using weak field measurements from Earth orbiting gravity probes. High throughput timing, hard X-ray spectroscopic and polarimetric measurements, e.g., the fast time variability of a relativistic Fe X-ray line or the energy and time dependence of the polarization angle of the accretion disk emission probe the strong field region and constrain the physical parameters of the compact object (mass and spin). Deviations from general relativity in the strong field limit can be studied in a way complementary to measurements by gravitational wave detectors such as LISA.
In addition, black holes and neutron stars provide a unique laboratory for studying matter under strong gravity, while neutron stars also allow the study of matter in the presence of extreme magnetic fields and at supra-nuclear densities. The structure of a neutron star is set by the nuclear equation of state, whose determination is one of the priorities of physics today. The composition of a neutron star can vary from neutrons and protons to hyperons - particles that contain strange quarks - and possibly even free quarks. X-rays emerging from the strongly curved space time of neutron stars encode information on the mass and radius of the compact object, hence the equation of state, EOS, of matter at supra-nuclear density. A large area, high spectral, and high time resolution X-ray telescope is required to constrain physics in the strong field and high density limit.
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