Two Fates of the Horizon: When a Black Hole Stops Breaking ✎ express

Original: "Horizon Singularities in the Schwarzschild Geometry of the Teleparallel Equivalent of General Relativity"
arXiv:2606.22121 · 2026-06-20 · arXiv non-exclusive · independent analysis · 2 min
Schwarzschild geometry in teleparallel gravity can be regular at the horizon: it all depends on hidden parameters.

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The Schwarzschild black hole is the simplest model in general relativity. But when you switch to teleparallel gravity (TEGR), where torsion replaces curvature, the horizon develops a problem. Some quantities built from torsion tend to infinity. It's as if the horizon is a tear in space, and the black hole as a whole object doesn't exist.

The authors discovered that everything depends on a hidden setting. Schwarzschild geometry in TEGR splits into two classes. In the first, singular class, the infinities are real — the horizon is cut out of the world. In the second, regular class, there are no infinities, and the horizon becomes an ordinary point through which motion can continue. This setting is the Lorentz sector, a part of geometry not visible in the metric but affecting torsion.

Torsion in TEGR is the analogue of curvature in Einsteinian gravity. It describes how spacetime 'twists' rather than bends.

The authors applied three independent methods: the inertial frame condition, coordinates that penetrate the horizon, and a regularity criterion for the horizon. All pointed to the same class of Lorentz sector functions for which the horizon remains calm. For this class, all torsion invariants are finite, and one can construct an analytic continuation beyond the horizon.

Inertial effects in teleparallel gravity are not eliminated by a simple choice of reference frame. Even in a 'proper' frame, contributions unrelated to real torsion may remain.

Thus, the Schwarzschild black hole in TEGR gains a second life. The horizon ceases to be a mathematical wall and becomes a passable boundary, as in Einsteinian theory. This discovery resolves a long-standing contradiction and shows that teleparallel gravity can describe black holes without pathologies if its internal degrees of freedom are properly accounted for.

In standard general relativity, the Schwarzschild horizon is a coordinate singularity that can be removed by a coordinate change. In TEGR, however, the singularity can be physical, and then the horizon is truly a 'hole' in space.

If the horizon is not a wall but a door, then traveling through a black hole ceases to be science fiction. In Carl Sagan's novel 'Contact,' the heroine travels through wormholes — perhaps with the right Lorentz sector, this could become reality.

Scientists
Fritz ZwickyJacob BekensteinKarl SchwarzschildStephen HawkingSubrahmanyan ChandrasekharRainer Weiss
Concepts
schwarzschild metric horizon area schwarzschild black hole inner horizon teleparallel gravity black hole singularity wald entropy naked singularity no-hair theorem Hawking area theorem modified gravity singularities EHT gravitational radius kerr metric gravastar Lorentz transformations topological invariant Birkhoff's theorem event horizon stability apparent horizon