Fast scrambling of mutual information in Kerr-AdS5

Abstract

Abstract We compute the disruption of mutual information in a TFD state dual to a Kerr black hole with equal angular momenta in AdS 5 due to an equatorial shockwave. The shockwave respects the axi-symmetry of the Kerr geometry with specific angular momenta L ϕ 1 $$ {\mathcal{L}}_{\phi_1} $$ & L ϕ 2 $$ {\mathcal{L}}_{\phi_2} $$ . The sub-systems considered are hemispheres in the left and the right dual CFTs with the equator of the S 3 as their boundary. We compute the change in the mutual information by determining the growth of the HRT surface at late times. We find that at late times leading up to the scrambling time the minimum value of the instantaneous Lyapunov index λ L min $$ {\lambda}_L^{\left(\min \right)} $$ is bounded by κ = 2 π T H 1 − μ L + $$ \kappa =\frac{2\pi {T}_H}{\left(1-\mu {\mathcal{L}}_{+}\right)} $$ and is found to be greater than 2πT H in certain regimes with T H and μ denoting the black hole’s temperature and the horizon angular velocity respectively while L + $$ {\mathcal{L}}_{+} $$ = L ϕ 1 $$ {\mathcal{L}}_{\phi_1} $$ + L ϕ 2 $$ {\mathcal{L}}_{\phi_2} $$ . We also find that for non-extremal geometries the null perturbation obeys L + $$ {\mathcal{L}}_{+} $$ < μ −1 for it to reach the outer horizon from the AdS boundary. The scrambling time at very late times is given by κτ * ≈ log S $$ \mathcal{S} $$ where S $$ \mathcal{S} $$ is the Kerr entropy. We also find that the onset of scrambling is delayed due to a term proportional to log(1 − μ L + $$ {\mu \mathcal{L}}_{+} $$ ) −1 which is not extensive and does not scale with the entropy of Kerr black hole.

Keywords

• AdS-CFT Correspondence
• Black Holes
• Black Holes in String Theory
• Gauge-Gravity Correspondence