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This exercise aims to provide a flavor of the expertise required for the SPIN project as well as giving you an idea of the work expected of you. If you choose to apply to work with me on this project then I will ask you to work through the exercise and send in your results before the interview with me. I provide a worked out solution so you are free to look at it to verify your own solution or to copy and past from it. However please keep in mind that the exercise mostly serves to give you an idea of the skills required to avoid signing up for more than you can handle.

Background

Numerical relativity solves Einstein's equations of General Relativity using supercomputers to predict for example how two neutron stars collide and how gravitational waves such as the ones detected by LIGO are generated in such events. Computer simulations require initial data that they then evolve forwarded in time using the computer. In General Relativity such initial data has to satisfy what is called initial data constraints that are typically of the form

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