What Is The Effect Of Rotation In The Size Of A Traversable Wormhole? (Quantum / Cosmology)

The rotating BTZ black hole is a solution of Einstein gravity in 2+1 dimensions with a negative cosmological constant Λ = – 1 l². The solution can be constructed from a quotient of global AdS3. Now, Xiao and colleagues considered a rotating eternal black hole in three dimensions (rotating BTZ) and studied the traversable wormhole produced by including a double trace deformation at the boundary.

“We explored the effects of rotation in the size of a traversable wormhole obtained via a double trace boundary deformation.”

— told Xiao, third author of the study.

For simplicity, they first considered a constant boundary coupling. They showed that, at fixed temperature, the size of the wormhole opening increases with the angular momentum. They also established a bound on information that can be transferred and showed that in a rotating background more information can be sent through the wormhole as compared to the non-rotating scenario. However, for the type of interaction considered, the wormhole closes as the temperature approaches the extremal limit.

Figure 1: Opening of the wormhole when interaction is turned only along the x1 direction. Temperature fixed T = 1/2π. Set g = 1, ∆ = 0.6, t0 = 0, and tf = 1. © Xiao et al.

Finally, they briefly considered a scenario where the boundary coupling is not spatially homogenous (i.e. it is non-homogenous) and showed how this is reflected in the wormhole opening. They found that the wormhole opening is peaked near x1 (as shown in fig 1), but due to the presence of rotation the maximum value of the opening is slightly shifted to the right (i.e. y – x1).

Reference: Caceres, E., Misobuchi, A.S. & Xiao, ML. Rotating traversable wormholes in AdS. J. High Energ. Phys. 2018, 5 (2018). https://link.springer.com/article/10.1007%2FJHEP12%282018%29005 https://doi.org/10.1007/JHEP12(2018)005

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