In solving the grand challenge problem remarkable progress have been made in the last decade. Nevertheless, physically adequate important binary black hole configurations with arbitrarily pointing spins, with sufficiently large mass rations or with high eccentricity are still missing from the initial data collections. In addition, the most widely used initial data generators produce a lot of spurious radiation that contaminates the time evolution of their initial data. The principal aim is to produce physically adequate and clean initial data for the missing generic type of binary black hole configurations by adapting radically new ideas.
In doing so our research will be guided by results covered in [1,2,3,4]. In particular, we intend to use the parabolic-hyperbolic and algebraic-hyperbolic form of the constraint equations as proposed in . In addition, we shall use a fully spectral numerical integrator developed by our research group in order to solve the constraints equations, in their evolutionary forms [2,3]. The latter is based on the use of elegant mathematical tools such as the Newman-Penrose “eth”-operator and a multipole expansion of the basic variables in terms of spin-weighted spherical harmonics. Due to the use of these elements the algebraic-hyperbolic and parabolic-hyperbolic forms of the constraints (these are, in their original form, partial differential equations) can be traced back to a set of non-linear ordinary differential equations (ODE) for the multipole expansion coefficients . During the term of the PhD program, we intended to generalize significantly the construction proposed in  in order to generate the desired generic type of binary black hole initial data configurations.
 I.Rácz, Constraints as evolutionary systems, Class. Quantum Gravity 33 015014 (2016)
 I.Rácz and J.Winicour, Toward computing gravitational initial data without elliptic solvers, Class. Quantum Grav. 35 135002 (2018)
 K.Csukás, I.Rácz: Numerical investigations of the asymptotics of solutions to the evolutionary form of the constraints, Class. Quantum Grav. 37 155006 (2020)
 I. Rácz: A simple method of constructing binary black hole initial data, Astronomy Reports 62 953-958 (2018)