concept

Wormhole

A wormhole is a hypothetical topological feature of spacetime connecting distant points.
26 related articles · 2 formulas · 6 who worked here

Description

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.

History

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.

How it works

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.

In practice

So far pure theory, but wormhole research advances quantum gravity and may one day underlie superluminal communications or travel.

Fun fact

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.

Concept graph →

Formulas

$$ds^2 = -e^{2\Phi(r)} dt^2 + \left(1 - \frac{b(r)}{r}\right)^{-1} dr^2 + r^2 d\Omega^2$$
A static wormhole metric with shape function b(r) and redshift function Φ(r).
What is in the formula
ds^2variableSpacetime interval squared — spacetime interval metre squared
\Phi(r)variableRedshift function — redshift function
b(r)variableShape function — shape function metre
rvariableRadial coordinate — radial coordinate metre
tvariableTime coordinate — time coordinate second
d\Omega^2variableSolid angle element squared — solid angle element
doperatorExterior derivative — differential operator
ds^2=-(1-\frac{2m}{\sqrt{r^2+\ell^2}})dt^2+(1-\frac{2m}{\sqrt{r^2+\ell^2}})^{-1}dr^2+r^2dω^2 · 2605.04631v1
$$\frac{d^2 r}{dz^2} = \frac{b - r b'}{2b^2} > 0$$
Geometric condition for wormhole throat existence violating null energy condition.
What is in the formula
rvariableradial coordinate of the throat — radial coordinate metre
zvariableproper distance along the throat — proper distance metre
bvariableshape function of the wormhole — shape function metre
d/dzoperatorderivative with respect to proper distance — ordinary derivative
d/droperatorderivative with respect to radial coordinate — ordinary derivative
\frac{d^2r}{dz^2}=\frac{b-rb'}{2b^2}>0 · 2605.14027v1

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