Kerr/CFT Traversable Wormhole with Fermionic Double-Trace Deformation

TL;DR

This paper constructs a traversable wormhole using fermionic double-trace deformation in Kerr/CFT, analyzing its traversability, energy conditions, and potential observable echoes in near-extremal Kerr black holes.

Contribution

It introduces a fermionic double-trace deformation framework within Kerr/CFT to open and analyze traversable wormholes, including effects of rotation and temperature.

Findings

Fermionic perturbations enable wormhole traversal even where bosonic fields are unstable.

Lower temperature reduces wormhole traversability, which vanishes at extremality.

Observable echoes with delay times bounded by black hole scrambling time are predicted.

Abstract

The construction of a traversable wormhole with double-trace deformation has been achieved so far by using boson fields as the perturbation. In this work, we study double-trace deformation with fermion fields in the two-sided Kerr background to open a traversable wormhole. We construct the fermionic double-trace deformation within the Kerr/CFT framework. We consider the near-horizon, near-extremal Kerr geometry, which is dual to a conformal field theory. The lack of fermionic superradiance let us describe the wormhole at every region, even at the off-axis region where bosonic field experiences instability due to superradiance. By choosing a certain coupling between the left and right boundaries, the two-point function is modified, and its first order correction contributes the negative energy to open the wormhole. The wormhole is most traversable when the perturbation is turned on at early times, with opening that depends on the mode's frequency, the black hole temperature, and the fermion mass. At late times, the average null energy has damped oscillation behavior until eventually reaches zero. Wormhole with lower temperature have less traversability and it is completely closed at extreme limit. On the other hand, rotation near extreme limit can increases the upper bound on information transfer up to the order of the entropy. Additionally, symmetrical effective potential bumps connected by the wormhole can produce observable echoes. We find that the echo time delay cannot exceed the scrambling time of the black hole.