Speaker
Description
In this talk, I will present recent progress in the 3+1 formulation of the metric teleparallel and symmetric teleparallel equivalents of general relativity, TEGR and STEGR. For TEGR, I will discuss the linearized Hamilton's equations and their hyperbolicity properties. Although the original system of differential equations is not hyperbolic, we show that it can be recast as a strongly hyperbolic system through suitable variable redefinitions and the addition of constraints. For STEGR, I will examine how different treatments of boundary terms affect the Hamiltonian and Hamilton's equations. Specializing the theory to spherical symmetry, we find that the resulting evolution equations are only weakly hyperbolic. We stress the importance of strongly hyperbolic systems for numerical relativity applications, and discuss ongoing attempts towards numerical modeling. I will conclude by outlining how these results may extend to more general gravitational models, including general teleparallel gravity, scalar-torsion theories, scalar-nonmetricity theories, and related extensions.