Solitary stars wandering too close to the supermassive black hole at the centre of their galaxy may become tidally disrupted, if the tidal forces due to the black hole overcome the self-gravity holding the star together. Depending on the strength of the encounter, the star may be partially disrupted, resulting in a surviving stellar core and two tidal arms, or may be completely disrupted, resulting in a long and thin tidal stream expected to fall back and circularize into an accretion disc (the two cases are illustrated on the cover of this thesis).

While some aspects of a tidal disruption can be described analytically with reasonable accuracy, such an event is the highly non-linear outcome of the interplay between the stellar hydrodynamics and self-gravity, tidal accelerations from the black hole, radiation, potentially magnetic fields and, in extreme cases, nuclear reactions. In the vicinity of the black hole, general relativistic effects become important in determining both the fate of the star and the subsequent evolution of the debris stream.

In this thesis we present a new approach for studying the relativistic regime of tidal disruptions. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. The method, though trivial to incorporate into existing Newtonian codes, yields very accurate results at minimal additional computational expense.

Equipped with this new tool, we set out to systematically explore the parameter space of tidal disruptions, focusing on the effects of the impact parameter (describing the strength of the disruption) and of the black hole spin on the morphology and energetics of the resulting debris stream. We also study the effects of general relativity on partial disruptions, in order to determine the range of impact parameters at which partial disruptions occur for various black hole masses, and the effects of general relativity on the velocity kick imparted to the surviving core. Finally, we simulate the first part of a tidal disruption with our code and then use the resulting debris distribution as input for a grid-based, general relativistic magnetohydrodynamics code, with which we follow the formation and evolution of the resulting accretion disc.