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The characteristic physical timescales near stellar-mass compact objects are measured in milliseconds. These timescales -- the free-fall time, the fastest stable orbital period, and stellar spin periods -- encode the fundamental physical properties of compact objects: mass, radius, and angular momentum. The characteristic temperature of matter in the vicinity of neutron stars is such that the principal electromagnetic window into their realms is the X-ray band. Because of these connections to the fundamental properties of neutron stars, X-ray timing studies remain today the most direct means of probing their structure and dynamics. While current X-ray observatories have revealed many relevant and fascinating phenomena, they lack the sensitivity to fully exploit them to uncover the fundamental properties of compact objects and their extreme physics. With this white paper, we summarize and highlight the science opportunities that will accompany an order-of-magnitude improvement in X-ray timing sensitivity, a goal attainable in the coming decade.
Certain classes of astrophysical objects, namely magnetars and central engines of supernovae and gamma-ray bursts (GRBs), are characterized by extreme physical conditions not encountered elsewhere in the Universe. In particular, they possess magnetic
Neutron Stars (NSs) are compact stellar objects that are stable solutions in General Relativity. Their internal structure is usually described using an equation of state that involves the presence of ordinary matter and its interactions. However ther
The advent of moderately high-resolution X-ray spectroscopy with Chandra and XMM promised to usher in a new age in the study of neutron stars: we thought we would study neutron stars like stars, with resolved absorption spectra revealing their surfac
Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well described by the atmosphere model of a passively cool
Structures of X-ray emitting magnetic polar regions on neutron stars in X-ray pulsars are studied in a range of the accretion rate, 10$^{17}$ g s$^{-1} sim 10^{18}$ g s$^{-1}$. It is shown that a thin but tall, radiation energy dominated, X-ray emitt