The Higgs vacuum in the presence of strong gravitational fields: curvature induced electroweak symmetry restoration

Abstract

I investigate the behaviour of the Higgs field in Schwarzschild spacetime by introducing a Planck-suppressed coupling between the Higgs field and the Kretschmann scalar, the leading curvature invariant in Ricci-flat geometries. I show that spacetime curvature modifies the Higgs effective potential, causing the vacuum expectation value to decrease continuously with increasing curvature. A critical curvature is derived at which the Higgs vacuum expectation value vanishes, signalling a curvature-induced restoration of electroweak symmetry. For Schwarzschild black holes, we obtain analytical expressions for the critical curvature, the corresponding phase-transition radius, and the Planck-curvature radius that marks the onset of quantum-gravity effects. These results identify a self-consistent region inside the event horizon in which electroweak symmetry is restored while the effective description remains applicable. The model provides a simple analytical framework linking strong gravitational fields to the Higgs vacuum through a single dimensionless curvature-Higgs coupling.