In BF-theory terms, apart from the structure group itself, gravity and Yang-Mills theory or electromagnetism are distinguished in the constitutive law, or the simplicity constraints. This is suggestive of a unified topological phase, which is broken into separate internal and external gauge theory, with clear, almost canonical preferences for the excitation B-field for either part. But what if...
Lorentz gauge theory of gravity with a symmetry breaking "Cartan khronon" field demonstrates its successful explanation for the $\Lambda$CDM model, with an emergent integration 3-form behaving as ideal dust. Within the chiral scheme of this theory, only the right-handed regime recovers the general relativity. A natural question that arises is what happens with the left-handed gravity? When...
We review the current state of the numerical relativity formalism for teleparallel theories of gravity and assess the hyperbolicity of the 3+1 decomposition of the equations of motion in the Hamiltonian formulation. For this, we analyse a simplified version of the analog to the ADM equations in the teleparallel equivalent of general relativity. We consider linear perturbations around a flat...
Dynamical evolution of self-interacting vector fields often faces instabilities and apparent pathologies when performing numerical simulations. By displaying a detailed analysis of the initial-value problem of the theory in the language of scalar-tensor theories, I will show that the former are actually due to the breakdown of the hyperbolicity of the theory (Tricomi-type or Keldysh-type). I...
