On Einstein–Rosen bridges or Wormholes: Connection of two points in spacetime, net flux of lines of force, multiply-connected space



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Excerpts from the link https://en.wikipedia.org/wiki/Wormhole


A wormhole or Einstein–Rosen bridge is a hypothetical topological feature that would fundamentally be a shortcut connecting two separate points in spacetime. A wormhole, in theory, might be able to connect extremely far distances such as a billion light years or more, short distances such as a few feet, different universes, and different points in time.

A wormhole is much like a tunnel with two ends, each at separate points in spacetime.


[From J.A. Wheeler who coined the term “Black Hole” and “Wormhole”]: “This analysis forces one to consider situations... where there is a net flux of lines of force, through what topologists would call "a handle" of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming a "wormhole".


According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole. In the Einstein–Cartan–Sciama–Kibble theory of gravity, however, it forms a regular Einstein–Rosen bridge.


(…) Such an interaction prevents the formation of a gravitational singularity.[clarification needed] Instead, the collapsing matter reaches an enormous but finite density and rebounds, forming the other side of the bridge.[16]


The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris in a 1988 paper.




A Wormhole between Tubingen, Germany and Boulogne-sur-Mer, France developed as an exact solution of Einstein's field equations



(map by GoogleMaps)


cf wikipedia image and legend:  Image of a simulated traversable wormhole that connects the square in front of the physical institutes of University of Tübingen with the sand dunes near Boulogne sur Mer in the north of France. The image is calculated with 4D raytracing in a Morris–Thorne wormhole metric, but the gravitational effects on the wavelength of light have not been simulated.[17]


From the following link cited by the above article of wikipedia:



"The wormholes described here are exact solutions of Einstein's field equations; they were developed by K. Thorne* to give a scientific foundation to the novel Contact by C. Sagan ([1]) (The story of this development is told in [2][3] gives the theoretical background)."


[3] paper available here



ds^2 = -dt^2 + dl^2 + (b_0^2+l^2)(d theta^2 + sin^2 theta d phi^2)



The wormhole from the outside

The wormhole from the outside

There, once again we look back towards the wormhole.



Almost at the throat

Boulogne sur Mer


"The wormhole shown here connects the place in front of the physics institutes of Tübingen University with the beautiful sand dunes near Boulogne sur Mer in the north of France (image source [4]). For the theoretical astrophysics personnel it is handy for short trips in their lunch hour."


Another reference site by wikipedia:





* Kip S. Thorne http://www.its.caltech.edu/~kip/




"Kip Stephen Thorne, (born June 1, 1940) is an American theoretical physicist, known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech) until 2009[2] and is one of the world's leading experts on the astrophysical implications of Einstein's general theory of relativity."



Einstein's Legacy, Celebrating 100 Years of General Relativity: L.Krauss, K.Thorne, F.Wilczek origins.asu.edu/panel-einstein…






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