A wormhole is a hypothetical topological feature of spacetime connecting distant points.A wormhole is a hypothetical structure allowed by general relativity that connects two points in spacetime like a handle. It could link distant regions of the same universe or different universes. To keep the hole open for passage, exotic matter with negative pressure is needed, violating the usual energy conditions.
In 1916, Ludwig Flamm, interpreting the Schwarzschild solution, proposed the idea of a 'wormhole'. Einstein and Rosen in 1935 described the bridge as a geometrized model of an elementary particle. The term 'wormhole' was introduced by John Archibald Wheeler in 1957 in the context of quantum foam. Modern interest revived after the paper by Morris and Thorne, which showed the possibility of travel provided exotic matter exists.
Einstein's equations link geometry (the Einstein tensor Gμν) to matter (the energy-momentum tensor Tμν). For a wormhole, the metric is given as ds² = -e^{2Φ(r)}c² dt² + dr²/(1 - b(r)/r) + r² dΩ². The absence of a horizon requires Φ(r) to be finite everywhere. Traversability imposes conditions on b(r) and Φ(r), and also requires violation of the null energy condition (negative energy). Quantum effects, such as the Casimir effect, provide such a possibility.
So far pure theory, but wormhole research advances quantum gravity and may one day underlie superluminal communications or travel.
If you looked through a wormhole, you could see a distorted, lens-like but recognizable image of the other end — perhaps a star or galaxy that would otherwise take millions of years to reach.
| ds^2 | variable | Spacetime interval squared — spacetime interval metre squared |
| \Phi(r) | variable | Redshift function — redshift function |
| b(r) | variable | Shape function — shape function metre |
| r | variable | Radial coordinate — radial coordinate metre |
| t | variable | Time coordinate — time coordinate second |
| d\Omega^2 | variable | Solid angle element squared — solid angle element |
| d | operator | Exterior derivative — differential operator |
| r | variable | radial coordinate of the throat — radial coordinate metre |
| z | variable | proper distance along the throat — proper distance metre |
| b | variable | shape function of the wormhole — shape function metre |
| d/dz | operator | derivative with respect to proper distance — ordinary derivative |
| d/dr | operator | derivative with respect to radial coordinate — ordinary derivative |





















