Abstract
Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.
Highlights
For two dimensional Jackiw-Teitelboim gravity [13, 14] the island rule has been derived by making use of replica trick [15, 16].1 In this context the island contribution is associated with the contribution of new saddle points in the Euclidean path integral
The island rule has been applied for yet another interesting two dimensional gravitational model known as CGHS [20] that admits two dimensional asymptotically flat black holes
The first model has no cosmological constant so that one has to deal with asymptotically flat black holes, while in the second one there is a negative cosmological constant leading to black hole solutions that are asymptotically AdS
Summary
We would like to extend the island formula for the entropy to the cases in which the gravitational action contains higher derivative terms. In a similar way the log divergent term in SvN,matter will be dropped out by the corrections which have root in the renormalization of the coupling constants of the higher derivative terms (λ’s in (2.10)), so we start with a four dimensional formula for the entropy in its full structure form, we end up with a finite term, SvN,fin at the end of the day. This should be thought of the semi-classical prescription that computes the fine grained entropy of a black hole when higher derivative terms are taken into account
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