A geometric construction of the Riemann scalar curvature in Regge calculus

Understand

The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity.

• We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry.
• This allows one to constructively measure the scalar curvature using only clocks and photons.
• Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers.