Secrets of the universe revealed by Einstein’s equations

Lars Andersson is at present Professor at Max Planck Institute for Gravitational Physics (Albert Einstein Institute) in Potsdam, Germany. He will be Visiting Professor at the Department of mathematics, KTH Royal Institute of Technology, Stockholm.

Despite the fact that Einstein’s general theory of relativity is almost 100 years old, it is not fully understood yet. The theory implies a description of the development of the universe, as well as individual events in space like black holes. However, the models, which are currently used by physicists, describe the physical reality only under limited, special assumptions. Solutions of Einstein’s equations under less restrictive assumptions are required in order to better understand the physical reality.

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 you throw a ball, knowing the ball’s initial position and speed, as well the strength of the gravitational field and the air resistance, you can calculate the ball’s trajectory.

The initial conditions for Einstein’s equations must satisfy the so-called constraint equations. Solutions for Einstein’s equations can only be found after having solved the constraint equations. At present, they can be solved for short time periods but not for longer ones. One of the goals of the project is to find more solutions of the constraint equations and describe their properties. Studying exotic phenomena, the so-called singularities, where the laws of physics don’t hold, is another goal. The most well-known such singularity is the Big Bang – the beginning of the universe.

Photo Max Planck Institute for Gravitational Physics