# Doktorandseminarium: Constraint equations in General Relativity

- Date:
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: David Lundberg
- Contact person: Volodymyr Mazorchuk
- Seminarium

Abstract:

The year 1915 Albert Einstein presented General Relativity (GR). The predicted black holes have been indirectly observed, the predicted gravitational waves have been recently directly observed, and the theory has been very useful in understanding Cosmology (citation needed). The Theory stands uncontested as the best description of Gravitation a full century later.

But the theory is also very interesting from the mathematical point of view. The governing equations in GR are called the Einstein Field Equations (EFE) and are notoriously difficult to solve. Although some analytical solutions were discovered early on, it remained an open problem how to solve the EFE in full generality. In 1952 it was shown that one could tackle them as a Cauchy problem where the initial data is "a space of constant time" that is evolved in time to a full space-time solution. The initial data can not be completely arbitrary, but has to satisfy a certain "constraint"-condition, and the question then is in general to find such initial data.

In the talk I will discuss the above in some more detail and then discuss how one can solve this "constraint", which is to say to solve the so-called "constraint equations" under various circumstances.