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New astrophysical instruments such as skA (square kilometer Array) and IXO(formerly Constellation X) promise the discovery of tens of thousands of newisolated rotating neutron stars (pulsars), neutron stars in low-mass X-raybinaries (LMXBs), anomalous X-ray pulsars (AXPs), and soft gamma repeaters(SGRs). Many of these neutron stars will experience dramatic density changesover their active lifetimes, driven by either stellar spin-up or spin-down,which may trigger phase transitions in their dense baryonic cores. More thanthat, accretion of matter onto neutron stars in LMXBs is believed to causepycno-nuclear fusion reactions in the inner crusts of neutron stars. Theassociated reaction rates may be drastically altered if strange quark matterwould be absolutely stable. This paper outlines the investigative steps thatneed to be performed in order to explore the thermal response of neutron starsto rotationally-driven phase transitions in their cores as well as to nuclearburning scenarios in their crusts. Such research complements the exploration ofthe phase diagram of dense baryonic matter through particle colliderexperiments, as performed at RHIC in the USA and as planned at the futureFacility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany.

Phase Transitions in Dense Baryonic Matter and Cooling of Rotating Neutron Stars