Abstract
We study the entanglement among sequential Hawking radiations in the Parikh-Wilczek tunneling model of Schwarzschild black hole. We identify the part of classical correlation and that of quantum entanglement in bipartite information and point out its imitated relation to quantum gravity correction. Explicit computation of n-partite information shows that it is positive (negative) for even (odd) $n$, which happens to agree with the holographic computation. The fact that entanglement in the mutual information grows with time mimics the second law of thermodynamics. Later we extend our study to the AdS black hole and find the total mutual information which includes the classical correlation is sensible to the Hawking-Page phase transition.
Highlights
In this letter, after reviewing mutual information in the framework of the ParikhWilczek model, we discuss its generalization to n-partite information
We study the entanglement among sequential Hawking radiations in the ParikhWilczek tunneling model of Schwarzschild black hole
We identify the part of classical correlation and that of quantum entanglement in bipartite information and point out its imitated relation to quantum gravity correction
Summary
Thanks to the nonthermal spectrum in the Parikh-Wilczek model, one expects some kind of entanglement or correlation between two successive emissions. The second term is seemed as the self correlation, which measures the maximum entropy a radiation could carry as if it collapsed into a small black hole This leaves us the last term as a candidate for the desired quantum entanglement. We consider a simplest situation of splitting a black hole into two and each has mass ω1 and ω2 This process is classically forbidden but quantum-mechanically possible via tunneling process in the Parikh-Wilczek model. Hawking entropy due to splitting is given by 4πω12 + 4πω22 − 4π(ω1 + ω2)2 = −8πω1ω2 We claim this loss of Bekenstein-Hawking entropy should be compensated by mutual information shared between these two sub-black holes. This exactly reproduces the classical correlation in the definition of mutual information.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
