Mathematicians Propose a 'Cut‑and‑Paste' Method to Join Two Black Holes into a Wormhole

Two mathematicians have produced a new theoretical construction showing how two black holes might be joined to form a wormhole by using a formal "cut‑and‑paste" technique and filling the junction with exotic matter. The work is mathematical and speculative, offering a concrete geometry‑driven example rather than empirical evidence of natural wormholes.

Who did the work? Farook Rahaman (Jadavpur University) and Arya Dutta (PhD student) developed the model and analyzed its stability. Their calculations outline one precise physical and geometric setup in which a thin‑shell wormhole could, in principle, appear.

What is the setup? The model uses a Kalb–Ramond background field — a tensor field that arises in some string‑theory contexts — with a nonzero vacuum expectation value (VEV) that breaks local Lorentz symmetry. That background modifies the standard black‑hole solutions. By taking two copies of this modified black‑hole geometry, excising regions and gluing the remaining boundaries together with a thin shell, the authors construct a traversable bridge between the two spacetimes. Exotic matter with unusual stress‑energy properties is placed at the seam to support the junction.

"The Kalb–Ramond field is a background tensor field that arises in string theory and violates the local Lorentz symmetry of spacetime, upon acquiring the Vacuum Expectation Value (VEV). A non‑minimal coupling between the Kalb–Ramond VEV and the Ricci tensor may give rise to a modified black hole solution. Considering two copies of such black holes, we construct a thin‑shell wormhole using the ‘Cut‑and‑Paste’ technique."

Key concepts explained. The Kalb–Ramond field, the VEV and the Ricci tensor are tensor quantities used to describe how values vary across spacetime. Breaking local Lorentz symmetry means the engineered region of spacetime does not obey the usual symmetry constraints, allowing modified black‑hole metrics. "Cut‑and‑paste" is a rigorous topological method for excising and gluing pieces of geometry to create a new manifold; here it is applied to black‑hole spacetimes.

Exotic matter and stability. To hold open the wormhole throat the model requires exotic matter—energy with properties unlike ordinary matter, including effective negative energy density in the thin shell. The authors evaluate stability and identify ranges of parameters (for example, throat radius and coupling constants set by the model) where the thin‑shell configuration can be stable. Under standard parameter choices used in many wormhole studies the configuration is unstable, but modest changes or reinterpretations of those parameters can produce a stable regime.

Limitations and significance. Many ingredients of the construction remain speculative: the particular tensor background, the physical realization of the exotic matter, and the choice of parameters. The proposal does not claim observational support; it provides a mathematically precise example that connects two previously separate mathematical frameworks—modified black‑hole solutions and thin‑shell topology—and broadens the catalogue of theoretical wormhole constructions.

Takeaway. This work is a clear, careful mathematical exploration showing that within a specific, albeit speculative, theoretical setting two black holes could be "cut and pasted" to form a thin‑shell wormhole. It advances theoretical understanding by combining methods from geometry, topology and gravitational physics, and by highlighting what new physical ingredients would be required for such a bridge to be viable.