Four-dimensional traversable wormholes and bouncing cosmologies in vacuum
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Springer
Received: January 7, 2019 Accepted: April 11, 2019 Published: April 16, 2019
Andr´ es Anabal´ ona,b and Julio Olivac a
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ib´ an ˜ez, Avenida Padre Hurtado 750, Vi˜ na del Mar, Chile b Max-Planck-Institut f¨ ur Gravitationsphysik (Albert-Einstein-Institut), Am M¨ uhlenberg 1, D-14476 Potsdam, Germany c Departamento de F´ısica, Universidad de Concepci´ on, Casilla 160-C, Concepci´ on, Chile
E-mail: [email protected], [email protected] Abstract: In this letter we point out the existence of solutions to General Relativity with a negative cosmological constant in four dimensions, which contain solitons as well as traversable wormholes. The latter connect two asymptotically locally AdS 4 spacetimes. At every constant value of the radial coordinate the spacetime is a spacelike warped AdS 3 . We compute the dual energy momentum tensor at each boundary showing that it yields different results. We also show that these vacuum wormholes can have more than one throat and that they are indeed traversable by computing the time it takes for a light signal to go from one boundary to the other, as seen by a geodesic observer. We generalize the wormholes to include rotation and charge. When the cosmological constant is positive we find a cosmology that is everywhere regular, has either one or two bounces and that for late and early times matches the Friedmann-Lemaˆıtre-Robertson-Walker metric with spherical topology and an exponential scale factor. Keywords: AdS-CFT Correspondence, Classical Theories of Gravity ArXiv ePrint: 1811.03497
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)106
JHEP04(2019)106
Four-dimensional traversable wormholes and bouncing cosmologies in vacuum
Contents 1
2 The spacelike warped AdS3
2
3 Wormhole-like slicing of AdS4
3
4 The wormhole solution
3
5 Absence of closed timelike curves
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6 Holographic renormalization
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7 Holographic stability
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8 The charged and spinning generalization
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9 Bouncing cosmologies
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10 Discussion
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1
Introduction
Wormholes have a long and rich history in physics and the pop culture. The idea was originally introduced by Einstein and Rosen [1]. The motivation was the description of particles as gravitational and electromagnetic fields without singularities. Nowadays we understand that the Einstein-Rosen bridge is just a part of the Kruskal extension of the Schwarzschild metric and that the non-singular bridge to other universe is non-travesable. Traversable wormholes are spacetimes that causally connect two far away regions by means of a throat. Despite the general interest in their existence, they are still not part of an accepted piece of knowledge within theoretical physics. This situation should change with this letter. Indeed, a major open problem in physics is whether wormholes can take place in physically sensible and simple circumstances. It is well-established that asymptotically flat gravity in four dimensions requir
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