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Wormhole Physics Quantum Wormhole Physics Summary Wormhole Physics Quantum Wormhole Physics Summary Wormhole Physics In Classical and Quantum Theories of Gravity S. Al Saleh A. Mahrousseh L.A. Al Asfar Department of Physics and Astronomey ,King Saud University The 100th Anniversary of General Relativity. The 30th of November, 2015 Wormhole Physics Quantum Wormhole Physics Summary Outline Wormhole Physics Introduction What are Wormholes? Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable wormholes Wormhole and Time Travel Quantum Wormhole Physics Preliminaries Mathematical and Physical Results Wormhole Physics Quantum Wormhole Physics Summary Outline Wormhole Physics Introduction What are Wormholes? Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable wormholes Wormhole and Time Travel Quantum Wormhole Physics Preliminaries Mathematical and Physical Results Wormhole Physics Quantum Wormhole Physics Summary Introduction • Einstein's Theory of general relativity is one of the most magnificent achievements humanity had ever encountered. It demonstrates the marriage between matter and background geometry. Matter and spacetime had became one! G µν = κT µν (1) • These equations (1) were published a 100 years from today [3]. Are known as the Einstein Field Equations.Although They are not the only equations for gravity. But they are the only tested ones.[10]. Wormhole Physics Quantum Wormhole Physics Summary Introduction Many solutions to (1) were found, a lot of them were very interesting and related to observations. But one solution was so strange that Einstein himself was very skeptical about. This solution is called the Schwazchild solution It predicted the existence of Black holes a very dense object having an enormous gravity even spacetime will not make sense because of it! Later, in 1935 Einstein and Rosen [4] studied the extension of Schwarzchild solution to predict an even stranger object, knows as Einstein-Rosen Bridge. Or what is known as a Wormhole. Wormhole Physics Quantum Wormhole Physics Summary i + r = 0 + J u 1 = 0 III = u i 0 II I v = −∞ IV − = 0 J u i − r = 0 Figure: Penrose diagram of the maximally- extended Schwarzchild solution, demonstrating two universes with an Einstein-Rosen Bridge . Wormhole Physics Quantum Wormhole Physics Summary Outline Wormhole Physics Introduction What are Wormholes? Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable wormholes Wormhole and Time Travel Quantum Wormhole Physics Preliminaries Mathematical and Physical Results • Despite the abstractness of this definition. It contain a lot of insight of the physics and geometry of a wormhole. This definition describes exactly what one pictures a wormhole to "look like" Wormhole Physics Quantum Wormhole Physics Summary Definition of a Wormhole • We can start with a mathematical definition of a wormhole, Definition ( Einstein-Rosen Bridge) A compact region of Minkowskian spacetime Ω is homeomorphic to R × Σ. Where Σ having non-trivial topology and boundary @Σ ' S2. All hyper surfaces Σ are spacelike/ The region Ω is called a Wormhole / Einstein-Rosen Bridge . Wormhole Physics Quantum Wormhole Physics Summary Definition of a Wormhole • We can start with a mathematical definition of a wormhole, Definition ( Einstein-Rosen Bridge) A compact region of Minkowskian spacetime Ω is homeomorphic to R × Σ. Where Σ having non-trivial topology and boundary @Σ ' S2. All hyper surfaces Σ are spacelike/ The region Ω is called a Wormhole / Einstein-Rosen Bridge . • Despite the abstractness of this definition. It contain a lot of insight of the physics and geometry of a wormhole. This definition describes exactly what one pictures a wormhole to "look like" Wormhole Physics Quantum Wormhole Physics Summary The picture that approximate what the previous definition describes: Wormhole Physics Quantum Wormhole Physics Summary • It is not required to have two separate spaces connected by an ER bridge. We can imagine such topologies forming with a single space. It is similar to folding a paper and making a "shortcut" route between two distant points. • This will make our spacetime multiply connected! Wormhole Physics Quantum Wormhole Physics Summary Outline Wormhole Physics Introduction What are Wormholes? Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable wormholes Wormhole and Time Travel Quantum Wormhole Physics Preliminaries Mathematical and Physical Results • In other words, the "bridge" connecting the two black holes will keep getting longer and longer at the speed of light. Such that no particle entering one side is able to cross the other one. Wormhole Physics Quantum Wormhole Physics Summary Schwazchild Wormholes • A paper by Wheeler and Fuller had shown that ER bridges resulting from Schwazchild solutions are unstable. They will pinch off very quickly at the speed of light. and Not allowing any information to pass through the other side [6]. Wormhole Physics Quantum Wormhole Physics Summary Schwazchild Wormholes • A paper by Wheeler and Fuller had shown that ER bridges resulting from Schwazchild solutions are unstable. They will pinch off very quickly at the speed of light. and Not allowing any information to pass through the other side [6]. • In other words, the "bridge" connecting the two black holes will keep getting longer and longer at the speed of light. Such that no particle entering one side is able to cross the other one. • In this theory, the gravitational singularity formed by a collapsing matter of the blackhole cannot form due to the coupling of spin of the fermions. Instead, the collapsing matter bounces back and forms an Einstein-Rosen Bridge as well. Hence, every black hole in Einstein -Cartan theory is a wormhole.[15] Wormhole Physics Quantum Wormhole Physics Summary Wormholes In Einstien-Cartan Theory • General Relativity is not the only theory of gravitation. Einstein-Cartan theory is an alternative one. It is a modification of EFE's by including how spin couples to the geometry of spacetime via changing its torsion. Wormhole Physics Quantum Wormhole Physics Summary Wormholes In Einstien-Cartan Theory • General Relativity is not the only theory of gravitation. Einstein-Cartan theory is an alternative one. It is a modification of EFE's by including how spin couples to the geometry of spacetime via changing its torsion. • In this theory, the gravitational singularity formed by a collapsing matter of the blackhole cannot form due to the coupling of spin of the fermions. Instead, the collapsing matter bounces back and forms an Einstein-Rosen Bridge as well. Hence, every black hole in Einstein -Cartan theory is a wormhole.[15] Wormhole Physics Quantum Wormhole Physics Summary Outline Wormhole Physics Introduction What are Wormholes? Can Einstein Rosen Bridges Allow Spacetime Travel ? Traversable wormholes Wormhole and Time Travel Quantum Wormhole Physics Preliminaries Mathematical and Physical Results Wormhole Physics Quantum Wormhole Physics Summary Traversable wormholes A Traversable wormhole is a wormhole that allow matter and information to cross from one mouth to the other one. Figure: Image of a simulated traversable wormhole that connects the square in front of the physical institutes of University of Tbingen with the sand dunes near Boulogne sur Mer in the north of France. Here the gravito-optical effects are ignored. • However, semi-classical theories of gravity that predicts more than 3+1 D of spacetime such as Gauss Bonnet gravity[12][7] predict the existence of trasversable wormholes with ordinary matter or even without matter! • Moreover, Brane cosmology theories allow traversable wormholes open by cosmic strings of negatives mass . [15] Wormhole Physics Quantum Wormhole Physics Summary Examples of Traversable Wormholes • Traversable wormholes seem not to exist naturally. As there is no known natural cosmological process that allows them to form (unlike black holes) • Moreover, Brane cosmology theories allow traversable wormholes open by cosmic strings of negatives mass . [15] Wormhole Physics Quantum Wormhole Physics Summary Examples of Traversable Wormholes • Traversable wormholes seem not to exist naturally. As there is no known natural cosmological process that allows them to form (unlike black holes) • However, semi-classical theories of gravity that predicts more than 3+1 D of spacetime such as Gauss Bonnet gravity[12][7] predict the existence of trasversable wormholes with ordinary matter or even without matter! Wormhole Physics Quantum Wormhole Physics Summary Examples of Traversable Wormholes • Traversable wormholes seem not to exist naturally. As there is no known natural cosmological process that allows them to form (unlike black holes) • However, semi-classical theories of gravity that predicts more than 3+1 D of spacetime such as Gauss Bonnet gravity[12][7] predict the existence of trasversable wormholes with ordinary matter or even without matter! • Moreover, Brane cosmology theories allow traversable wormholes open by cosmic strings of negatives mass . [15] • Wormholes do not only connect two distinct spacelike points in one universe. They could link distinct "times" or spacetime points in multiverse. For example, if the spacetime is multiply connected at the quantum information inside a blackhole could " leak out " to other universes by going into a wormhole. Wormhole Physics Quantum Wormhole Physics Summary Examples of Wormholes • In General Relativity however, it is required to have wormholes made from exotic matter to be stable and allow transportation. Such wormholes are knows are Morris-Torn wormholes [18] [14] Wormhole
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