Matter under extreme conditions: X-raying black holes and neutron stars

"Black holes and neutron stars provide a unique laboratory to study matter under extreme gravity. Crucial predictions of general relativity in this regime, such as the existence of a minimum distance around a compact object inside which no stable orbit exists and, ultimately, the reality of the event horizon in black holes, have not yet been verified. On the other hand, the extremely dense core of a neutron star may contain strangeness-bearing baryons or deconfined quarks under conditions not attainable elsewhere. In this talk I will discuss, in a tutorial manner, different ways in which we can use X-ray observations to explore these issues, I will present some of the most recent developments in this field, and discuss how the Indian satellite ASTROSAT could help addressing these topics."