On the Existence and Utility of Rigid Quasilocal Frames

Understand

The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion.

• An RQF is defined as a two-parameter family of timelike worldlines comprising the boundary (topologically R x S^2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines be expansion- and shear-free.
• In other words, the size and shape of the system do not change.
• In previous work, such systems in Minkowski space were shown to admit precisely the same six degrees of freedom of rigid body motion that we are familiar with in Newtonian space-time, without any constraints, circumventing a century-old theorem due to Herglotz and Noether.