On the breakdown of space–time in general relativity

Based on the canonical quantization of d > 2-dimensional general relativity (GR) via Dirac constraint formalism (also termed as ‘constraint quantization’), we propose loss covariance a fundamental property theory. This breakdown occurs for first-order Einstein–Hilbert action, whereby diffeomorphism invariance, besides first-class constraints, second-class constraints also exist leading to non-standard ghost fields that render path integral non-covariant. We attempt, first time, calculation equivalent Hamiltonian formulation GR, which only exist. However, still in this action due invariance and structures arising from non-covariant integral. In contrast, find symmetry is restored with perturbative calculations possible weak limit gravitational field these actions. Hence, establish, space–time GR itself its limitation, indicating it be an effective theory (EFT). further non-perturbative feature strong Besides note preserved when conducted non-Abelian gauge theories, such Yang–Mills These findings are novel gravity EFT approach, consistent singularity theorems, yet extend them, theorems indicate at black holes. Our contrast asymptotic safety program. They support emergent theories gravity, though unique, they do not require thermodynamics entropic From view, new degrees freedom and(or) principles sector full requirement, broken high-energy (strong field) GR.