Ayan BanerjeeJadavpur University

At the beginning of the 20th century, Albert Einstein revolutionized the idea that space and time do not exist as separate , rather it is a combination of space and time to a single abstract universe i.e. space, consisting of three dimensions and time is said to have only one dimension.

Space-time

Einstein said we can think of these space-time as fabric.

In physics, a wormhole is a hypothetical topological feature of space-time that is essentially a "shortcut" through space and time. A wormhole has at least two mouths which are connected to a single throat. If the wormhole is traversable, matter can 'travel' from one mouth to the other by passing through the throat.

What is Wormhole ?

Traveling through a wormhole takes less time than traveling between the same distance in normal space.

Traversable wormholes would allow travel in both directions from one part of the universe to another part of that same universe (called intra-universe) very quickly or would allow travel from one universe to another (called inter-universe) .

The name "wormhole" comes from the following analogy used to explain the phenomenon: imagine that the universe is the skin of an apple, and a worm is travelling over its surface, then distance from one side of the apple to the other is equal to half of the apple's circumference. The worm has to travel is considerably less, if it burrows a wormhole directly through the apple, instead of stayingon the apple's surface.

Types of Wormholes

Lorentzan wormholes (general relativity)

Mainly studied by experts in Einstein gravity

metric with signature (-1, +1, +1, +1)

Euclidean wormholes (particle physics)

metric with signature (+1, +1, +1, +1)

Mainly studied in quantum gravity theory

Einstein introduced his general theory of relativity, in 1916, which still remains the standard model for gravitation. In the year1935, Einstein and his collaborator Nathan Rosen investigated the possibility of obtaining an atomistic theory of matter and electricity. They wanted to know how general relativity would treat individual particles, and hoped somehow it can account for quantum phenomena. This phenomenon known as an "Einstein-Rosen bridge".

History of the Wormhole

However, in 1962 John A. Wheeler and Robert W. Fuller showed that Einstein-Rosen bridge space-time structure was highly unstable in field-free space, and that it will pinch off too quickly before a single photon could be transmitted through it. This work lead to find different kinds of wormholes. The possibility of traversable wormholes in general relativity gathered pace by the publication of a paper in 1987, “Wormholes in space-time and their use for Interstellar travel: A tool for teaching general relativity”, by Michael Morris and Kip Thorne which is known to us a Morris-Thorne wormhole.

Simplified their analysis by first assuming the existence of a suitably well-behaved geometry.

The solution must every where obey the Einstein field equations. It is assumed that GR is correct.

The matter and fields that generate the wormhole’s space-time curvature must have a physically reasonable stress-energy tensor or not.

Morris-Thorne Wormholes

The metric for a static spherically symmetric space-timeis given by

b(r) called the “shape” function since it determines the spatial shape of the wormhole.

Φ(r) called the “red shift” function since it determines the gravitational red shift.

As is the throat radius, so =

Traversability criteria: For traversable wormhole, there should not be any horizons present i.e. must be finite everywhere.

frame, (with c = G = 1) we obtain the following stress-energy scenario.

Einstein Field Equations

Einstein field equation, in an orthonormal

Where is the energy density, is the radial pressure, and is the lateral pressure measured in the orthogonal direction to the radial direction.

Stress-Energy at the Throat

at the throat, the tension exceeds the total mass-energy density.

Materials with the property is called, “exotic”.

fundamental condition in wormhole physics is the violation of the NEC. i.e.Matter that violates the NEC is denoted as exotic matter.

Research Zone

Stabilizing a wormhole with exotic matter.

Minimize Exotic matter.

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