Yordan Petkov

Continuous-time and tent-move numerical evolution in Regge calculus

Started Mar. 6, 2026

Abstract or project description

This project will investigate and redevelop the continuous-time 3+1 evolution in Regge calculus, which has not seen new development since the 80s and 90s, to the standard tent-move evolutions widely used like PIES. The theoretical work will examine wether the continuous-time equations can be derived as a limit of the 4D covariant formulation, and it will also explore connections to the ADM decomposition to clarify the meaning of lapse, shift, extrinsic curvature and constraint equations in Regge calculus. Both continuous-time and tent-move algorithms will be implemented in Julia and tested on known spacetime solutions. Convergence to the continuum solutions will be tested, as well as numerical stability, speed and efficiency. The aim is to determine whether continuous-time Regge is practical for numerical relativity and two establish a formal relationship between the two Regge calculus methods and standard numerical techniques.