Einstein–Cartan theory with torsional geometry predicts stable black-hole remnants that retain information and link to Higgs-field physics

Einstein–Cartan theory with torsional geometry predicts stable black-hole remnants that can retain information and link it to Higgs-field physics

One of modern physics’ most profound mysteries - the “black-hole information paradox” - may at last have an elegant answer. The proposed solution could also offer insight into how fundamental particles acquire mass.

During the 1970s, Stephen Hawking demonstrated that black holes emit faint radiation and therefore slowly evaporate. Yet, under quantum mechanics, this process appears to destroy information, contradicting the principle of unitarity. A new study instead takes an approach based on the geometry of space with extra dimensions.

Torsion prevents complete black-hole evaporation

The researchers examined the implications of Einstein–Cartan gravity, formulated in seven dimensions on a mathematical structure known as a “G2-manifold with torsion”. Unlike standard General Relativity, this framework permits not only the curvature of spacetime but also its twisting, or torsion. At Planck densities - the maximum matter density predicted by quantum mechanics - this torsion generates a repulsive force that stops a black hole from evaporating entirely. Rather than vanishing, it leaves behind a stable “remnant” with a mass of roughly 9 × 10⁻⁴¹ kg.

According to the researchers, this remnant serves as an archive, preserving information as “quasinormal modes” of the torsion field. A remnant produced by a black hole with the Sun’s mass could hold approximately 1.515 × 10⁷⁷ qubits of information, enough to resolve the paradox.

Extra dimensions and the Higgs field

The study also connects the model to elementary-particle physics. When the geometry is reduced from seven to four dimensions, it accounts for the origin of the electroweak scale (~246 GeV), which is associated with the Higgs field responsible for particle masses. In this setting, the vacuum expectation value of the torsion field matches the electroweak scale.

Why have extra dimensions not yet been detected? Particles associated with them have masses of around 8.6 × 10¹⁵ GeV, far beyond the reach of the Large Hadron Collider. Nevertheless, the theory makes testable predictions. For instance, stable black-hole remnants could form part of dark matter. Their gravitational signatures, or evidence of seven-dimensional geometry in the cosmic microwave background and gravitational waves from the early Universe, could support the model.