The universality of islands outside the horizon

Abstract

We systematically calculate the quantum extremal surface (QES) associated with Hawking radiation for general D-dimensional (D ≥ 2) asymptotically flat (or AdS) eternal black holes using the island formula. We collect the Hawking radiation particles by a non-gravitational bath and find that a QES exists in the near-horizon region outside the black hole when c • G (D) is smaller enough where c is the central charge of the conformal matter and G (D) the D-dimensional Newton constant. The locations of the QES in these backgrounds are obtained and the late-time radiation entropy saturates the two times of black hole entropy. Finally, we numerically check that the no island configuration exists once c•G (D) exceeds a certain upper bound in two-dimensional generalized dilaton theories (GDT).

Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes

“…In this manner, one might assume that the s-wave approximation mentioned in refs. [6,33,35,43] can be applied. 9 In other words, after the expansion of the matter fields in terms of the spherical harmonics on the large sphere, one can have both massless and massive Kaluza-Klein modes.…”

“…The advantage of working with the Kruskal coordinates is that the state on the whole Cauchy slice, i.e. the black brane plus the baths, is the vacuum state [9,33], and hence one can simply apply the EE formula for the case where the matter QFT is in the vacuum state (See e.g. eq.…”

“…In this manner, the Kruskal coordinates can be defined as follows for the two baths (see also refs. [9,33,43])…”

“…Second, replica wormhole saddle which is a wormhole connecting various copies of the original black hole. It was observed that the replica saddle leads to the contribution of the islands and enforces the entropy Furthermore, the island rule have been explored extensively for various black holes in flat and AdS spacetimes such as: JT gravity [9,[17][18][19][25][26][27][28], two-dimensional dilaton gravity [29][30][31][32][33] , in higher dimensions [33][34][35][36][37][38][39][40][41][42], higher derivative gravity theories [43], charged black holes [44][45][46][47], pure BTZ black hole microstates 3 [48][49][50], and black holes coupled to gravitating baths [50][51][52][53]. See also [4] for a very nice review on the topic.…”

Island, Page Curve and Superradiance of Rotating BTZ Black Holes

“…Therefore, we can understand the island paradigm more clearly by eternal black holes. Later, the island formula (1.1a) was extensively applied to other backgrounds, such as Jackiw-Teitelboim (JT) gravity [15][16][17][18][19], two-dimensional asymptotically flat spacetime [20][21][22][23][24], higher-dimensional spacetime [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], and gravitating baths [43][44][45]. Furthermore, the island is also studied in the BCFT model [46][47][48][49][50] and cosmology [51][52][53][54][55].…”