Space has seven dimensions, and a physics model published in March 2026 proposes that the extra ones, the four you cannot see, feel, or measure with any existing instrument, are the reason black holes do not destroy information when they die.
Findings published in General Relativity and Gravitation in March 2026 quantify a stable black hole remnant mass of approximately 9 × 10⁻⁴¹ kilograms, an object so small it makes a single proton look enormous, produced entirely by the geometry of hidden spatial dimensions that have been curled up inside every point in the universe since the Big Bang.
Most people are aware that the universe has three spatial dimensions: length, width, and depth. General relativity, Einstein’s theory of gravity, adds a fourth, time. String theory and related frameworks in theoretical physics have long proposed that the universe actually has more dimensions than those four, additional spatial directions that are not absent but compactified, meaning coiled so tightly around themselves at scales far below the atomic that nothing we have ever built can probe them directly. The question of how many extra dimensions exist, what shape they take, and what physical effects they produce has been one of the central open problems in theoretical physics for decades. This model proposes that the answer is seven total spatial dimensions, with three compact extra ones arranged in a specific geometric structure called a G2-manifold, and that this structure directly produces two of the most important numbers in all of physics.
A G2-manifold is not a shape you can draw. It is a seven-dimensional geometric object defined by a specific type of internal symmetry, classified mathematically in the same way that a sphere or a torus is classified, but existing in a number of dimensions that has no visual analogue in everyday experience. The critical property of a G2-manifold for this model is that its geometry is not perfectly smooth. It carries something called torsion, a twisting of the spatial fabric that goes beyond ordinary curvature. In standard general relativity, space curves around mass but does not twist. Torsion adds a second type of geometric deformation, like the difference between a bent rod and a wrung cloth. At normal energy scales torsion produces effects too small to detect. At the extreme densities found inside a collapsing black hole in its final moments, the twisting force torsion generates becomes large enough to halt the collapse entirely.
The seven-dimensional structure this model uses is built on a product of two simpler shapes: a three-sphere, which is the three-dimensional surface of a four-dimensional ball, combined with a four-sphere, the four-dimensional surface of a five-dimensional ball. Written in mathematical shorthand this is S³ × S⁴. The model is not claiming these are literally the shapes of the universe’s extra dimensions. The authors are explicit that this is a proof-of-concept geometry chosen because it has exactly the mathematical properties needed to demonstrate the mechanism. What matters is that within this specific seven-dimensional framework, torsion acquires a preferred stable configuration, a value called the vacuum expectation value of the scalar torsion field, written as τ₀. The geometry of those seven dimensions forces τ₀ to settle at a specific energy level, and the value it settles at is 246 GeV.
That number is not a coincidence inserted to make the model work. It is the electroweak scale, one of the most precisely measured values in all of particle physics, the energy at which the weak nuclear force and the electromagnetic force separate from each other, the scale that governs how the W and Z bosons acquire their mass through the Higgs mechanism. Physicists have measured this value to extraordinary precision in accelerator experiments. The seven-dimensional geometry of this model produces it from pure mathematical structure, without needing to borrow it from experiment. The shape of the hidden dimensions locks in the energy scale that controls particle physics in our four-dimensional world.
From that single geometric output, 246 GeV, a second number follows directly. The remnant mass of an evaporated black hole is calculated by squaring τ₀ and dividing by the Planck mass, the fundamental unit of mass at which quantum gravity effects become dominant, approximately 1.22 × 10¹⁹ GeV. The calculation gives 9 × 10⁻⁴¹ kilograms. A proton masses 1.67 × 10⁻²⁷ kilograms, so the remnant is roughly one hundred trillion times lighter than a proton. It is the smallest stable object the model permits to exist, held in place not by any ordinary force but by the geometry of dimensions too small to observe.
Understanding why this remnant matters requires understanding the problem it solves. In 1974, Stephen Hawking calculated that black holes radiate energy slowly and steadily, losing mass particle by particle over timescales far longer than the current age of the universe. The radiation carries no information about what fell into the black hole. A star that collapsed to form the black hole billions of years ago leaves no trace in the outgoing radiation. Neither does anything that fell in afterward. When the black hole finishes evaporating, according to Hawking’s original calculation, everything is gone. That is a direct contradiction of quantum mechanics, which requires that information cannot be destroyed, only rearranged. The contradiction is the black hole information paradox, and it has resisted resolution for fifty years.
The seven-dimensional model resolves it by preventing the evaporation from completing. As a black hole shrinks toward zero mass, the torsion field in the extra dimensions produces an increasingly powerful repulsive force. At Planckian densities the repulsion exactly balances gravity. The black hole cannot shrink further. It freezes at 9 × 10⁻⁴¹ kilograms and stays there permanently. Every piece of matter that fell into the black hole over its entire lifetime excited specific patterns in the torsion field inside those seven dimensions. Those patterns are trapped in the remnant as quasi-normal modes, vibration states of the torsion field that behave like the resonant frequencies of a bell. Each combination of infalling matter excites a unique pattern. The specific set of excited modes, their frequencies and amplitudes, constitutes a complete record of everything that ever crossed the event horizon.
The storage capacity of those modes is not assumed to be sufficient. It is calculated from first principles. The torsion field oscillations are trapped inside a cavity whose size is set by the compactification radius of the extra dimensions, approximately 3.9 × 10⁻³² metres, far smaller than any particle. Counting the number of distinct oscillation states that fit inside that cavity and calculating their total information capacity gives a remnant entropy of 4π × M²_BH / M²_Pl, where M_BH is the mass of the original black hole and M_Pl is the Planck mass. For a black hole originally the mass of the Sun, that expression equals approximately 1.515 × 10⁷⁷ qubits. The Bekenstein-Hawking entropy of a solar-mass black hole, the standard measure of its total information content calculated from its event horizon area, is also approximately 10⁷⁷. The seven-dimensional geometry produces exactly the right number.
The remnant survives indefinitely because of a property called topological protection, rooted in the structure of the G2-manifold. Topology in physics refers to properties of a geometric shape that cannot be changed by any smooth, continuous transformation. You can deform a coffee cup into a donut without tearing it, because both have one hole. You cannot deform either into a sphere, because a sphere has none. The remnant in this model carries a topological charge, a conserved quantity tied to the winding structure of the G2-manifold’s geometry. Transitioning from a state with non-zero topological charge to a state with zero charge, meaning a state where the remnant ceases to exist, requires passing through a configuration that costs infinite energy. Ordinary quantum mechanical processes cannot do it.
Quantum tunnelling, which allows particles to cross energy barriers that classical physics says are impassable, is in principle a route around topological protection. The model calculates the tunnelling rate and finds it suppressed by a factor of approximately e^(-2 × 10³⁵), a number with roughly ten to the thirty-fifth zeros after the decimal point before you reach the first non-zero digit. The age of the observable universe is approximately 4.3 × 10¹⁷ seconds. The remnant’s tunnelling decay rate makes that timescale irrelevant. For all physical purposes, the remnant does not decay.
One of the more striking features of the seven-dimensional framework is what it predicts about the extra dimensions themselves. The lightest particle associated with the compactified extra dimensions, called the lightest Kaluza-Klein excitation, would have a mass of approximately 8.6 × 10¹⁵ GeV. The Large Hadron Collider operates at a maximum collision energy of around 1.3 × 10⁴ GeV. The gap between these numbers is six orders of magnitude: the extra-dimensional particles predicted by this model are a million times heavier than the most energetic collisions the LHC produces. No current or planned particle accelerator operates anywhere near the energy needed to produce or detect them. The model is consistent with everything particle physics has measured to date precisely because the effects of the extra dimensions only become visible at energies no experiment can currently reach.
The corrections to standard Hawking radiation from the torsion field are negligible at all stages except the final Planckian phase. This means the model preserves every verified prediction of standard black hole physics throughout the billions of years of a black hole’s life, only intervening at the very last instant to halt the complete evaporation. The electroweak precision tests that constrain extensions to the Standard Model, specifically the S and T parameters that physicists use to measure deviations from known particle behaviour, receive corrections from this seven-dimensional geometry on the order of 10⁻²⁹, thirty orders of magnitude below current experimental sensitivity.
The model’s authors identify its current limitations directly. The S³ × S⁴ topology is a controlled theoretical environment rather than a claim about the actual geometry of the universe’s extra dimensions. A complete derivation of this geometry as a stable vacuum solution of M-theory, the eleven-dimensional framework that unifies the various versions of string theory, has not been carried out. The treatment of the internal seven-dimensional geometry as rigid and unaffected by the intense spacetime curvature near a black hole is an acknowledged simplification. A first-principles statistical count of the remnant’s microstates from the oscillation modes has been outlined but not fully completed.
What the model currently provides is a geometrically grounded, internally consistent, parameter-free framework in which two of physics’ central unsolved problems connect to the same mechanism. The electroweak scale emerges from the shape of seven-dimensional space. The black hole information paradox is resolved by the same geometry. The remnant mass is 9 × 10⁻⁴¹ kilograms, set by the ratio of the electroweak scale to the Planck scale, stable against every known decay channel, storing approximately 1.515 × 10⁷⁷ qubits for a solar-mass progenitor. The information is not destroyed. It is held in dimensions you cannot see.
Source:
Pinčák, R., Pigazzini, A., Pudlák, M., & Bartoš, E. (2026). Geometric origin of a stable black hole remnant from torsion in G2-manifold geometry. General Relativity and Gravitation, 58, 29. https://doi.org/10.1007/s10714-026-03528-z
