Where is the center of mass of a star – and what does this have to do with mathematics?

(Carla Cederbaum, University of Tübingen)

Einstein’s theory of General Relativity from 1915 describes, how space and time combine to a curved spacetime that has to satisfy the so-called Einstein equations. According to the Einstein equations, “the distribution of matter determines the curvature of the spacetime and the curvature of spacetime determines the motion of the matter” (J. Wheeler). A black hole, a star, or a galaxy will then be described by special solutions of the Einstein equations. After a brief recollection of General Relativity and the mathematical ideas involved in it such as curvature I will address the question where the center of mass of a star, a galaxy, or a black hole lies – and why this question is so difficult to answer. I will also sketch the mathematical methods that are used to define the center of mass.