Numerical Relativity and the Binary Black Hole Problem — Miguel Alcubierre

The field equations of General Relativity describe the geometry of spacetime, that is the gravitational field, in the presence of concentrations of mass and energy. Even if they are conceptually quite elegant, in practice these equations are extremely complex and difficult to solve. When one wants to study the gravitational field associated with realistic astrophysical systems that involve strong and dynamic gravitational field becomes necessary to use numerical simulations. In this talk I will discuss the basic ideas behind numerical relativity, and particularly the history of its application to the problem of the collision of binary black holes and the prediction of their gravitational wave emission.