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  1. 1. Ayan BanerjeeJadavpur University
  2. 2. Space-time At the beginning of the 20th century, Albert Einsteinrevolutionized the idea that space and time do not exist asseparate , rather it is a combination of space and time to asingle abstract universe i.e. space, consisting of threedimensions and time is said to have only one dimension. Einstein said we can think of these space-time asfabric.
  3. 3. What is Wormhole ? In physics, a wormhole is a hypothetical topological feature ofspace-time that is essentially a "shortcut" through space and time.A wormhole has at least two mouths which are connected to asingle throat. If the wormhole is traversable, matter can travelfrom one mouth to the other by passing through the throat. Traversable wormholes would allow travel in both directionsfrom one part of the universe to another part of that sameuniverse (called intra-universe) very quickly or would allow travelfrom one universe to another (called inter-universe) . Traveling through a wormhole takes less time than travelingbetween the same distance in normal space.
  4. 4.  The name "wormhole" comes from the following analogy used toexplain the phenomenon: imagine that the universe is the skin of anapple, and a worm is travelling over its surface, then distance fromone side of the apple to the other is equal to half of the applescircumference. The worm has to travel is considerably less, if itburrows a wormhole directly through the apple, instead of stayingon the apples surface.
  5. 5. 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
  6. 6. History of the Wormhole Einstein introduced his general theory of relativity, in1916, which still remains the standard model forgravitation. In the year1935, Einstein and his collaboratorNathan Rosen investigated the possibility of obtaining anatomistic theory of matter and electricity. They wanted toknow how general relativity would treat individualparticles, and hoped somehow it can account for quantumphenomena. This phenomenon known as an "Einstein-Rosen bridge".
  7. 7.  However, in 1962 John A. Wheeler and Robert W.Fuller showed that Einstein-Rosen bridge space-timestructure was highly unstable in field-free space, andthat it will pinch off too quickly before a single photoncould be transmitted through it. This work lead to finddifferent kinds of wormholes. The possibility oftraversable wormholes in general relativity gatheredpace by the publication of a paper in 1987, “Wormholesin space-time and their use for Interstellar travel: A toolfor teaching general relativity”, by Michael Morris andKip Thorne which is known to us a Morris-Thornewormhole.
  8. 8. Morris-Thorne Wormholes Simplified their analysis by first assuming the existence of asuitably well-behaved geometry. The solution must every where obey the Einstein fieldequations. 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.
  9. 9.  The metric for a static spherically symmetric space-timeis given by b(r) called the “shape” function since it determines thespatial shape of the wormhole. Φ(r) called the “red shift” function since it determines thegravitational red shift.
  10. 10.  As is the throat radius, so = Traversability criteria: For traversable wormhole, thereshould not be any horizons present i.e. must be finiteeverywhere. Einstein Field EquationsEinstein field equation, in an orthonormalframe, (with c = G = 1) we obtain the followingstress-energy scenario.
  11. 11. Where is the energy density, is the radialpressure, and is the lateral pressure measured in theorthogonal direction to the radial direction.
  12. 12. Stress-Energy at the Throat at the throat, the tension exceeds the totalmass-energy density. Materials with the property is called, “exotic”. fundamental condition in wormhole physics is theviolation of the NEC. i.e.Matter that violates the NEC is denoted as exotic matter.
  13. 13. Research Zone Stabilizing a wormhole with exotic matter. Minimize Exotic matter.
  14. 14. Thank you