By Dave DeFusco
Could a tunnel through space and time鈥攍ong a dream of science fiction鈥攅ver 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, , 鈥淭hin-shell Wormhole with a Background Kalb鈥揜amond Field,鈥 explored a mathematical model of a wormhole鈥攁 hypothetical shortcut through spacetime that could, in theory, connect two distant regions of the universe. 鈥淎 wormhole allows faster-than-light travel or even time travel,鈥 said Dutta. 鈥淚t hasn鈥檛 been observed yet, but theoretical research has advanced a lot.鈥
A wormhole, he said, can be formed by joining two black holes together鈥攂ut with their singular, infinitely dense cores removed鈥攕o that matter and light could pass smoothly from one end to the other. The tricky part is keeping the tunnel open. 鈥淭o build a wormhole, you need a very unusual kind of matter that has negative energy-density,鈥 said Dutta. 鈥淚t鈥檚 not like normal matter; it鈥檚 more like dark energy or dark matter.鈥
Scientists call this exotic matter, and minimizing the amount needed is key to making a stable wormhole. That鈥檚 where Dutta鈥檚 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 鈥渕embrane鈥 called the throat. 鈥淭he idea is to concentrate the exotic matter in a very small area,鈥 he said. 鈥淭hat might make it more stable.鈥
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鈥揜amond 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.
鈥淭his field modifies gravity in a special way, giving rise to a different kind of black hole,鈥 said Dutta. 鈥淲e asked: if the black hole geometry changes, what happens when we join two of them together to form a wormhole?鈥
Using a mathematical method known as the cut-and-paste technique, he literally 鈥渃ut out鈥 the singularities鈥攖he problematic cores of two black holes鈥攁nd 鈥減asted鈥 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鈥檚 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. 鈥淚t鈥檚 about how a particle would move radially from somewhere around the wormhole throat,鈥 he said. 鈥淎t small radii, it鈥檚 pulled in but beyond a certain radius, it鈥檚 pushed outward.鈥
Though wormholes and the Kalb鈥揜amond field remain purely theoretical, Dutta鈥檚 work helps bridge two powerful ideas鈥擡instein鈥檚 theory of general relativityand string theory鈥檚 extra-dimensional fields鈥攊nto one elegant mathematical framework. Looking ahead, he hopes to analyze how light would bend around such a wormhole using the Gauss鈥揃onnet theorem, which could provide clues about what an observer might see if these mysterious tunnels ever existed.
鈥淚f we study light deflection,鈥 he said, 鈥渨e can learn much more about the wormhole鈥檚 geometry and physical nature.鈥
