As the endpoints of massive star evolution, neutron stars are enigmatic celestial objects characterized by extremely dense and exotic nuclear matter, magnetospheres with positrons (antimatter), rapid rotation and ultra-strong magnetic fields. Such an extreme environment has provided an accessible astrophysical laboratory to study physics under conditions unattainable on Earth and to tackle a range of fundamental questions related to: the aftermath of stellar evolution and the powerful explosions of massive stars, the equation of state and physics of some of the most exotic and magnetic stars in the Universe, the workings of the most powerful particle accelerators in our Galaxy and beyond, and the sources of gravitational waves that are yet to be detected. Recent observations revealed a great diversity of neutron stars, including ultra-strongly magnetized pulsars, referred to as magnetars, and unusual types of accreting X-ray pulsars. In this white paper, we highlight the prospects of the upcoming X-ray mission, ASTRO-H, in studying these highly magnetized neutron stars.
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