Emergent field theory

Abstract: The uniqueness theorems for general relativity and Yang-Mills theories can be circumvented by dropping the ubiquitous, yet often implicit, assumption that physical fields, such as the spacetime metric, are fundamental. The novel concept of emergent fields makes it possible to construct modified theories of gravity and forces where the spacetime metric and strength tensor fields emerge from a covariance analysis in the canonical formulation with nontrivial relations to the fundamental phase space and no additional degrees of freedom are required. This is an example of a post-Einstein-Yang-Mills theory that implies new physics. In particular, explicit realizations of the theory in symmetry-reduced systems have shown robust resolutions of the singularities that plague the classical theories in regions of extreme spacetime curvature, including nonsingular (SU(2)xU(1)-charged) black holes with a cosmologial constant and collapsing solutions, as well as Gowdy and FLRW cosmologies. Further applications include modifications in the spectrum of quasinormal modes and in the evaporation process of black holes, as well as relativistic formulations of long-range gravitational effects capable of modeling MOND as an alternative solution to the dark matter problem. New results here include an extension of the spherically symmetric system that couples SU(2) gauge fields and the generalization of previous dynamical, homogeneous solutions.