The Behavior of Matter Under Extreme Conditions A White Paper Submitted to the Astro 2010 Decadal Survey of Astronomy and Astrophysics

The cores of neutron stars harbor the highest matter densities known to occur in nature, up to several times the densities in atomic nuclei. Similarly, magnetic field strengths can exceed the strongest fields generated in terrestrial laboratories by ten orders of magnitude. Hyperon-dominated matter, deconfined quark matter, superfluidity, even superconductivity are predicted in neutron stars. Similarly, quantum electrodynamics predicts that in strong magnetic fields the vacuum becomes birefringent. The properties of matter under such conditions is governed by Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED), and the close study of the properties of neutron stars offers the unique opportunity to test and explore the richness of QCD and QED in a regime that is utterly beyond the reach of terrestrial experiments. Experimentally, this is almost virgin territory.