By Dave DeFusco
Could a tunnel through space and time—long a dream of science fiction—ever exist in theory? According to Arya Dutta, a Ph.D. student in Mathematics at the Katz School, the answer might be yes, at least on paper.
Accepted for publication in the International Journal of Geometric Methods in Modern Physics, , “Thin-shell Wormhole with a Background Kalb–Ramond Field,” explored a mathematical model of a wormhole—a hypothetical shortcut through spacetime that could, in theory, connect two distant regions of the universe. “A wormhole allows faster-than-light travel or even time travel,” said Dutta. “It hasn’t been observed yet, but theoretical research has advanced a lot.”
A wormhole, he said, can be formed by joining two black holes together—but with their singular, infinitely dense cores removed—so that matter and light could pass smoothly from one end to the other. The tricky part is keeping the tunnel open. “To build a wormhole, you need a very unusual kind of matter that has negative energy-density,” said Dutta. “It’s not like normal matter; it’s more like dark energy or dark matter.”
Scientists call this exotic matter, and minimizing the amount needed is key to making a stable wormhole. That’s where Dutta’s focus comes in. He studied a special type called a thin-shell wormhole, where the exotic matter is confined to an extremely thin region, essentially a mathematical “membrane” called the throat. “The idea is to concentrate the exotic matter in a very small area,” he said. “That might make it more stable.”
To create his wormhole, Dutta started with two modified black hole geometries influenced by a background field from string theory, which is the theoretical framework that tries to unite gravity with quantum mechanics. This background field, known as the Kalb–Ramond field, is a kind of tensor field that can change the structure of spacetime itself. When it takes on a constant background value, it breaks a fundamental symmetry of nature called Lorentz symmetry, which states that the laws of physics are the same for all observers moving at constant speeds.
“This field modifies gravity in a special way, giving rise to a different kind of black hole,” said Dutta. “We asked: if the black hole geometry changes, what happens when we join two of them together to form a wormhole?”
Using a mathematical method known as the cut-and-paste technique, he literally “cut out” the singularities—the problematic cores of two black holes—and “pasted” the remaining spacetime surfaces together. The result was a new theoretical construction: a thin-shell wormhole in a Lorentz-violating spacetime.
Dutta then examined how the wormhole’s physical properties, such as pressure, energy density and stability, changed when the Lorentz-violating parameters, which measure how strongly the field distorts spacetime, were varied. He found that his model violated the weak and null energy conditions, confirming that exotic matter is needed to keep it open, but it still satisfied the strong energy condition, a rare and intriguing result.
His analysis also revealed that smaller wormholes act attractively, pulling objects inward, while larger ones become repulsive, pushing them away. “It’s about how a particle would move radially from somewhere around the wormhole throat,” he said. “At small radii, it’s pulled in but beyond a certain radius, it’s pushed outward.”
Though wormholes and the Kalb–Ramond field remain purely theoretical, Dutta’s work helps bridge two powerful ideas—Einstein’s theory of general relativityand string theory’s extra-dimensional fields—into one elegant mathematical framework. Looking ahead, he hopes to analyze how light would bend around such a wormhole using the Gauss–Bonnet theorem, which could provide clues about what an observer might see if these mysterious tunnels ever existed.
“If we study light deflection,” he said, “we can learn much more about the wormhole’s geometry and physical nature.”
