A Close Look at the Theory of Relativity

Professor Mattias Dahl will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Differential Geometry and Relativity Theory Group at the Department of mathematics, KTH Royal Institute of Technology, Stockholm.

Albert Einstein’s theory of general relativity describes how the gravity shapes the universe. The theory has proven very successful and has been confirmed by a large number of measurements with a high degree of accuracy. However, the equations defy solution except in special cases.

One way to look at the theory is to formulate Einstein’s equations as a so-called initial value problem. This approach means that if we can describe the state of (for example) the universe at a given moment, the equations will fully predict its evolution over time. Simple examples of such solutions can be found in classical mechanics. If one throws a ball, and if one knows the ball’s initial position and speed, as well the strength of the gravitational field and the air resistance, one can calculate the ball’s trajectory.

One complication for the theory of general relativity is that the initial conditions for Einstein’s equations must satisfy the so-called constraint equations. One can find solutions for Einstein’s equations only after having solved the constraint equations first. At present, one can solve the constraint equations for short time periods but not for longer ones. Are the black holes tied to situations where the equations lose their validity? Do other exotic phenomena, the so-called singularities, in which the laws of physics no longer describe the physical reality, exist? The most well-known such a singularity is the Big Bang – the beginning of the universe. One of the goals of the project is studying such singularities. Another goal is to find more solutions of the constraint