📝 SummarXiv

Abstract

The Higgs field is conventionally treated as a small local perturbation atop a large, constant vacuum value that uniformly permeates the universe. I propose instead that in regions of extreme gravitational intensity -- such as near gravitational singularities -- the Higgs field behaves in a profoundly non-perturbative manner. In such environments, spacetime and the Higgs field engage in a dynamic interplay that extends spacetime beyond the singularity, achieving geodesic completeness. The continuation beyond the singularity is dominated by antigravity effects, reshaping the causal structure of spacetime and enabling novel flows of matter and information, including traversal through singularities. In its standard form, the combined framework of the Standard Model (SM) and General Relativity (GR), as well as most of its extensions, fails to capture these phenomena due to its geodesic incompleteness. By contrast, a refined, locally conformal-symmetric formulation -- denoted i(SM+GR) -- naturally incorporates these effects. GR is not an optional component of i(SM+GR) but an essential ingredient. This framework preserves the empirical success of SM+GR in the low-energy regime while predicting striking new phenomena in extreme gravitational settings, including within black holes (on both sides of the singularity) and in pre--Big Bang cosmology. At the classical field theory level, i(SM+GR) offers fresh perspectives on the black hole information puzzle and provides a platform for locally scale-invariant generalizations, such as geodesically complete quantum field theory, string theory, and unified models of fundamental interactions. This paper presents the detailed derivations and explanations that underlie a condensed letter version recently published in [1].