1. Objective of numerical relativity is to develop simulation code and relating computing tools to solve problems of general relativity and relativistic astrophysics. Numerical relativity lab. course – welcome. The word “numerical relativity” is used for the simulations which involve dynamical spacetime evolution, and in which one can not simplify the Einstein equation using symmetry to avoid solving constrained dynamics. Numerical relativity is used in highly non-linear regime, and generic spacetime for which analytic method (or approximations) can not be used.

2. Numerical relativity lab. course – welcome. Problems motivated from the importance in relativistic astrophysics: 1. Binary neutron star merger and subsequnet formation of a hypermassive neutron star or a black hole. 2. Binary black hole merger. 3. Black hole –neutron star binary merger, and a massive disk formation. 4. Heavy stellar core collapse to a proto-neutron or a black hole formation. (relating to the supernova, or hypernova.) 5. Dynamical or secular instability of a rapidly rotating neutron star. These phenomena are considered as the sources of Short  -ray burst (1, 3) Long  -ray burst (4) Gravitational waves (all of the above). Problems motivated from classical or mathematical general relativity: Critical phenomena. Existence of the solution of Einstein equation.

3. Initial data preparation (Elliptic eq.) Time evolution: Einstein-Euler system, or GRMHD (Hyperbolic eq., also solve Gauge eq.) Micro physics, (neutrino, radiation, magnetic field, Realistic EOS) GW extraction, BH horizon finder Computing elements in numerical relativity. Analysis of the simulated data (GW spectrum, merger remnant) Visualization

4. ° Plan for the numerical relativity course – Practical aspects. However, the instructor may not have know ledges about many of the above. Exploit web resources for an easy solution. Self-teaching and sharing of knowledge of each other are requested. Practically learn skills of the scientific computing (and skills of the scientific research) from a collaboration for developing numerical codes in numerical relativity. Those skills may include basic know ledges of : Operating systems, mainly Unix, and associated tools. Computing language, FORTRAN90/95, Mathematica, (debugger, MPI…) Graphics and visualization. Documentation for the code collaboration. Writing a paper (if we could produce a substantial results). Instructor's role for these aspects is more for tutoring and coordination. Always think about what kind of contributions that you could make.

5. ° Plan for the numerical relativity course – class organizaton. Roughly 1/2 of the class would be used for actual coding – practical learning for the computing. 1 st stage– making the initial data code for a rapidly rotating compact star. In practice, refer to some FORTRAN 77 codes (written by me), develop a code in FORTRAN90/95. (Learning numerical methods as well as FORTRAN90/95.) 2 nd stage – Develop a simulation code following standard formulations, and/or try more difficult initial data code. Roughly 1/4 of the class would be used for status report of each of you, discussion and coordination to proceed the code collaboration. Roughly 1/4 of the class would be used for lecturing theory, physics, math and numerical methods necessary for the numerical relativity. For those who wish to have deep understand of the numerical relativity would have to go through (many) original papers. (A list of references should be made. ) 1. 2. 3.

6. ° Planning of computer simulations. First of all, one should check that the problem you are going to solve is (astro)physically (or scientifically) well motivated or not. 0. 2. Grasp what kind of physics is involved in the problem. ex) What kind of physics should be used in the problem (GR necessary)? What kind of time/length scales are involved? Is any simplification/analytic method for the problem available? 1. Evaluate if the simulation is the most effective solution for the problem. ex) usually, it is difficult to go beyond the dynamical time scale for the simulations check if the current computing resources is enough for our purpose. Software: Hardware: Memory, CPU.