Frontiers in Numerical Gravitational Astrophysics
2^nd Course of the International School on Astrophysical Relativity

«John Archibald Wheeler»

      The  meeting has the format of an advanced school, where high level scientists speak of their work in the field of the study of gravitating systems in Astrophysics, both on the classic and relativistic side, keeping their lectures at a level clearly understandable to graduate students.

      The objective of the course is to learn from Newtonian physics and to extend this knowledge to Relativistic computational astrophysics. Physical examples in the course will begin with computational Newtonian dynamics both for single stars (initial instability and core formation through accretion, final evolutionary phases and collapse, supernovae) and stellar systems (open and globular clusters, galaxies). We will then move to relativistic computational physics. Every Session of the School  will  face a topic on two parallel (Newtonian and Relativistic) points of view. 

      The initial collapse and fragmentation of a molecular cloud leads to star formation. Physics is higly non-linear, and gravity is strongly coupled to microphysics. General Relativity is usually not considered relevant in this context, because the fate of a massive gas cloud, almost free falling dissipatively, is not commonly studied. But this may be one of the origins of black holes.

      With regard to star collapse and explosion, the methods in the Newtonian and the Relativistic versions of discretization are very similar. However, differences arise between the two Newtonian and the Relativistic approaches, mainly because of the coordinate invariance of General Relativity.     

     The dynamics of stellar systems, even in presence of massive black holes in their centers, usually relies on integration of Newtonian equations of N interacting objects. The methods are mainly devoted to both numerical accuracy and time consumption reduction; in any case, attention should be given to a proper physical treatment (relativity) when dealing with the phenomenon of mass accretion around the singularity. This is indeed a still open problem, fundamental into the definition of supermassive black formation and accretion and Active Galactic Nuclei genesis.

    The freedom of choice of coordinates in Relativity means that intuition about physical effects becomes complicated. Poor coordinate choices may appear innocuous, but can have severe effects on the long-term evolution of a system. A substantial aspect of the course will be the study of different coordinate choices. Additionally, formulations of General Relativity must be carefully considered for their behavior under perturbation (i.e. the hyperbolicity of the system, which determines how the solutions react to inevitable small computational errors).

      At the same time as the discussion of astrophysics proceeds, various approaches to discretization and solution of the computational equations (finite arithmetic, N-body approach) will be described. Actually, modern results in both classical and relativistic regimes are beyond analytic treatment and require sophisticated numerical algorithms. Furtherly, realistic astrophysical simulations are so demanding computationally as to be necessarily implemented on huge parallel computing platforms. Carrying out such simulations involves a substantial supercomputing challenge.