  General relativity (GR) admits two alternative formulations with the same
dynamics attributing the gravitational phenomena to torsion or nonmetricity of
the manifold's connection. They lead, respectively, to the teleparallel
equivalent of general relativity (TEGR) and the symmetric teleparallel
equivalent of general relativity (STEGR). In this work, we focus on STEGR and
present its differences with the conventional, curvature-based GR. We exhibit
the 3+1 decomposition of the STEGR Lagrangian in the coincident gauge and
present the Hamiltonian, and the Hamiltonian and momenta constraints. For a
particular case of spherical symmetry, we explicitly show the differences in
the Hamiltonian between GR and STEGR, one of the few genuinely different
features of both formulations of gravity, and the repercussions it might
encompass to numerical relativity.
